Thor would be a likely candidate. Since he is Loki's brother, he already has a connection with him. Thor might be the one to convince the other Avengers to give Loki a chance and be the first to reach out and try to befriend him in this new situation.
He would probably interact a lot with Thor. Since they are brothers, there is a pre - existing relationship full of complexity. Also, he might interact with Iron Man quite often. Tony Stark's sarcastic nature and Loki's trickery could lead to some really interesting exchanges, either in the form of verbal sparring or working together on some high - tech and magic - combined projects.
Loki could also provide the Avengers with valuable information about otherworldly threats. Since he has connections to different realms, he may know about an upcoming invasion. In return for his help, he could demand that the Avengers clear his name for some of his past misdeeds, leading to an interesting dynamic between them in the fanfiction.
One idea could be that Loki gets turned into a vampire while in the midst of his schemes against the Avengers. This new state gives him different powers and motives. He might struggle with his newfound thirst and also use his vampire abilities to outwit the Avengers in different ways.
If Loki impersonated Thor, the real Thor would be furious when he found out. The other Avengers, like Iron Man, might initially be confused but then quickly realize something is off. Iron Man would likely use his technology to detect the impostor. Hulk might just smash first and ask questions later when he senses something wrong with 'Thor'.
One popular 'tony saves loki fanfiction' might be 'The Rescue Mission' where Tony uses his high - tech gadgets to save Loki from a dangerous situation in an alternate universe. It's a really exciting read.
Maybe the Avengers are trying to prevent a powerful artifact from being misused. Loki, who has a history with artifacts, offers his assistance. He might do this to gain some sort of favor from the Avengers or because he realizes the consequences of the artifact falling into the wrong hands. In the fanfiction, he could use his trickery to steal the artifact back from the villains before they can use it.
One interesting Loki and Avengers fanfiction could be where Loki is forced to team up with the Avengers against a greater threat. Maybe an ancient evil that even Loki realizes is too dangerous to face alone. He grudgingly works with them, and along the way, there are lots of humorous exchanges as the Avengers don't trust him at first.
Thor is an obvious choice. Their complex brotherly relationship offers a lot of material for fanfiction. They can have intense emotional scenes, from arguments to reconciliations. For example, in a story where Loki is on the verge of doing something really bad, Thor's attempts to stop him can be very engaging.