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Hi anon! The short answer is no, I don’t think it’s possible, has never been. There is so much speaking against it - so here’s the long answer (stating the obvious):

Let's start with looking at Historia's reasons for becoming pregnant in the first place. Usually the reason for having a child is love. It's crystal clear though that this is not the case for Historia's child, no matter who the father is. The only one who Historia showed genuine affection towards was Ymir, and ever since her death Historia didn't really seem to care about anyone except for the orphan kids of Paradis. Now, chapter 138 confirmed that Eren was/is in love with Mikasa, or - if you don't see it that way - at least that Mikasa is the most important person in his life, so important that he would even ditch his best friend Armin and send Historia through hell just to spend his last years with Mikasa and Mikasa alone. Eren never showed similar feelings towards anyone but her, and the special moments he shared with her are plenty. Her memory shards always take up the most space by far and they're almost always at the very center. So, Eren and Historia both have (or had) their special someone whom they don't want to live without, and once they're separated from them their characters become dark. This makes Eren and Historia pretty similar to each other, and it's exactly why they became allies, or "partners in crime" even. They do care for each other, but not at all in a romantical way. Rather, we know that Eren cares for all of his friends and the people of Paradis in general. He wants them to live long and happy lives, so it's only natural that he initially stood up against Zeke's plan to turn Historia into a breeding machine and have her titanized eventually. He desperately sought a way out of it because it was against every single principle he has and because Historia is one of his dearest friends, but not his lover. Historia appreciated this, but she had actually accepted her fate and was willing to go through that hell if it served a greater good. Which is why it was no surprise that she was the one to suggest the pregnancy later while Eren had despised the idea the whole time.

So, if love isn't the reason for Historia's pregnancy, what is? Actually, there are several tactical reasons for it, and none of them requires Eren to be the father.

As mentioned above, Historia was the one to suggest the pregnancy, when she was talking with Eren about his Rumbling plans. We haven't seen the whole talk (yet), but I think we've seen enough to understand what it all meant. In short, the whole purpose of her pregnancy was to avoid her being titanized and Zeke being fed to her. While Eren initially just wanted to save her from having to bear a child she clearly didn't want and to stop the cruel cycle of children having to eat their parents, he now also had something different in mind. He needed a titan of royal blood to put his plan into action, and conveniently his half-brother was just that. However, Zeke would have been fed to Historia the moment he lay a foot on Paradis if the military had their way, and that may have even been an option for Eren too, since she’s got royal blood just as well as Zeke. But Historia actually wasn't okay with Eren's plans at first and even wanted to go along with the military's. So he needed to convince her to obey, otherwise he would have had to use Founding Titan to make her cooperate - whereas he had seen in his future memories that with Zeke he would be able to achieve his goal much easier. Moreover, had he used Historia instead of Zeke, her lifespan would have been shortened drastically, and not only that: It would've put her in grave danger. We don't know exactly how much Eren knew about the future, but even if he hadn't known anything at all at that time, he must've considered the possibility of his plan failing. Maybe he even already knew he was gonna be killed, and if it had been Historia in Zeke's place during the Rumbling, she would've been killed along with him. Eren did everything he possibly could to leave his friends out of his plans, to be the only one responsible for it all, to be the only "bad guy" - that's what the Rumbling was all about in the first place. He needed Historia to play along, but quietly. Well, Historia made it pretty clear she wouldn't support him with the Rumbling, so much so that Eren offered to alter her memories if the burden of knowing was too much for her to bear. However, when he reminded her of her own words, that she was "the worst girl in the world", humanity's enemy, I guess Historia knew in that moment that she wouldn't be able to stop him, so she gave up opposing him and became his ally again. Since the only option to prevent Historia from being titanized and eating Zeke was the pregnancy, in the end, it was a choice between certain death (either in the near future or after 13 years at the latest) or a 9-month-hell for Historia, and they chose the latter as it obviously seemed like the smaller price to pay.

So now they had agreed on the pregnancy being necessary as a way to prevent Historia's certain death and to start the Rumbling. I can see why some people think it'd be logical that Eren would "help" her with executing this plan, but there is way too much speaking against that:

- As I have made clear above, Eren and Historia are not in love, have never been. In fact, they are or were both in love with someone else. It is therefore highly unlikely that Eren would just say "sure you need a baby I'll make you one" - no, both of them would never ever want this. If you think they would, you haven't understood their characters at all. Besides, Historia may have given in to Eren's plan after all, but keep in mind that she was actually wholeheartedly against his ideas. While they were allies in the end, their mindsets were quite different, if not opposing. That's why I don't see that "connection" that some fans claim exists between them. They are very similar in character, but they deal with their fates very differently.

- I've highlighted before that Eren despises the idea of putting Historia through the living hell that is forced pregnancy. Do you really think he would even be able to have sex with her like that? The only reason he agreed to her becoming pregnant is that the only other option was her certain death. If there had been another way, he sure as hell would never have agreed to put her through that.

- I haven't mentioned him until now but he's probably even the most important piece in this puzzle: Farmer-kun exists. Why would Historia even bother to approach Farmer-kun if she really already had Eren to make her a child? He wouldn't be necessary. Some say he's just a "cover-up story", but what for? Why would Eren and Historia even have to keep it a secret if Eren was the father? That one military officer said it loud and clear when talking to Nile and the others: they do not care at all who impregnated Historia. The queen is free to chose her suitors herself. All they care about is the simple fact that she's pregnant. She could've even said she didn't know who the father was, it wouldn't have changed a thing. Moreover, consider the fact that Farmer-kun seems oblivious to all of it. If he really was a cover-up, he wouldn't know, and that means Historia would still have had to sleep with him to make him believe he's the father, even if she already was pregnant from Eren. And if Eren really was in love with Historia, he would never let her have sex with someone else just for cover-up. As if the pregnancy itself wasn't enough of a burden already.

- Last but not least: Eren does not have any special genes at all. He's not of royal blood, nor is he an Ackermann or Asian or anything that would make him a tactical choice for being the father of this child. Titan powers are not inherited by shifter's children either - it was stated unmistakably in the manga that when a shifter dies without passing on their titan powers, they're transferred to a random newborn Eldian child, no matter the distance or blood relation between the two. From this perspective, Farmer-kun's genes are just as good as Eren's.