Awww this ask is so sweet. ♥ Here’s how I imagine it would go down:

Loki would be baffled and embarrassed and afraid that Thor is going to leave him because there’s no way he would understand why Loki had to transform into a wolf while Thor was away on business in another realm several weeks ago. (Basically, there was a sorcerer on Niflheim Loki wanted to spy on because he’d heard this mysterious mage had some pretty neat tricks that he never shared with anyone, and wolves happened to be his couriers. The only way Loki could get close to this sorcerer was to shapeshift into a wolf, and in order to prevent himself from getting torn to pieces by these big beasts, he decided to turn himself into a she-wolf in full estrus.)

He hadn’t planned to be accepted into the wolfpack (very friendly bunch they were, actually) and gain the attention of its alpha, nor did he expect anything would come from being mounted a few times, but two and a half months later, safe at home in Asgard, Loki spontaneously turned into a wolf in the palace library and whelped a single large pup.

Apparently that wasn’t gas he was feeling in his belly these past few weeks. Oh dear.

Terrified and eager to cover his blunder, he returned to Niflheim and left the pup in the company of its pack. Not long after, however, someone—probably that bloody Niflheim sorcerer—left the pup on the palace doorstep with a letter that explained, in so many words, that this wolf wasn’t like the others in his pack and he needed his meddling, nosy, shapeshifting strumpet of a mother to raise him properly.

Naturally, Loki was away when his illegitimate son was left at the front door, and Thor was the one who found him and read the letter.

He is absolutely ecstatic. 

“A wolf-son!” he bellows, lifting the pup proudly. “Look at him, Loki! He has your eyes! Can we raise him together? Does he have a name? No? Then I shall call him Fenrir! Look at our boy, Loki! Isn’t he great?”

Loki is speechless. (And a little relieved, to be honest.)

Fenrir—aka Fen, aka Fenny, aka Son—becomes the apple of Thor’s eye. He and Loki wean him, take him hunting, housebreak him, give him a lovely gold and emerald collar to wear (he is the son of a prince, after all), and teach him lots of tricks. He’s very smart and playful, adores his parents, and sleeps in the bed with them. 

Loki isn’t too happy about that. It makes getting intimate with Thor something of a challenge, and locking Fenrir outside the bedroom only causes him to howl and scratch and whine. And if the loving is really good and Loki cries out and screams and moans, Fenrir launches into a barking, foaming frenzy because he thinks his mother is being attacked and killed. Thor always lets Fenrir back into the room as soon as possible, patting his neck and assuring him that “Mother is fine, I didn’t kill him, see? Everything is alright.”

It still doesn’t solve the problem with all the hair in the bedsheets. 

Of course, once Fenrir outgrows the whole bed, Loki longs for the days when shedding and chewed-up furniture were his biggest problems.