Sure. Fanfiction often plays with the normal roles of characters. If Naruto were Minato's sensei in a fanfic, it might start with Naruto coming from an alternate future or having some special knowledge. This could create unique interactions between them, for example, Naruto might teach Minato some of the skills he learned from Jiraiya in a different way.
A possible plot could involve Naruto being reborn in an alternate timeline where he has all his memories and abilities from his previous life. As Minato's sensei, he could use his knowledge of the future to prevent certain tragedies. He might teach Minato advanced ninjutsu techniques and also instill in him a sense of unity among the ninja clans. This could change the course of history in the Naruto world, with Minato becoming an even more powerful and wise leader under Naruto's tutelage.
Minato would likely focus on Naruto's natural strengths. Since Naruto has a large chakra reserve, Minato could teach him how to better utilize it in combat. This might involve creating more powerful and complex jutsu combinations. Minato could also introduce Naruto to strategic thinking in battles. He might set up mock battles where Naruto has to think on his feet and come up with creative solutions. And of course, Minato would train Naruto in the use of his signature jutsu, like the Rasengan, but with his own unique twists and improvements.
Perhaps Naruto, as Minato's sensei, could focus on teaching Minato about the importance of bonds. Minato was always a bit of a loner in terms of his natural talent. Naruto could show him how his friends and comrades are his greatest strength. This could lead to Minato making different decisions in his life, such as being more open with his teammates and relying on them more in battles.
Naruto would probably be a very encouraging sensei. He has always been someone who believes in others. So, he would constantly be motivating Minato, telling him that he can achieve great things no matter the odds. In contrast, some other senseis in the Naruto universe can be quite strict and demanding, with a more 'tough love' approach. Naruto's style would be more about building confidence.
In the fanfiction, Naruto's new sensei could be a mysterious figure who has ties to the Sage of Six Paths. This person might have been waiting for the right time to appear and train Naruto. They could possess knowledge about the origin of chakra and how to fully unlock Naruto's power. It could also be someone who was once an enemy but has now changed their ways and wants to use their skills to train Naruto for the greater good of the ninja world.
There's a chance that Naruto's new sensei could be a self - taught ninja who has developed their own unorthodox style. This person sees Naruto's ability to think outside the box and wants to refine that in him. They could introduce Naruto to a new way of looking at chakra control and combat strategies that are completely different from what he has been taught so far.
I think Orochimaru would be the most unexpected sensei. Usually, he's seen as a villain, but in a fanfiction, if he were to train Naruto, it would be extremely unexpected. He has a vast knowledge of jutsu, especially forbidden ones. He could teach Naruto some very powerful and unique abilities, but at the same time, Naruto would have to deal with Orochimaru's morally ambiguous nature.
One popular theme is Minato getting to know Naruto in the afterlife. Since Minato died when Naruto was a baby, fanfictions often explore their relationship in a spiritual realm.
In fanfiction, Naruto and Minato often represent a connection between generations. Minato was a great ninja in his time, and Naruto is following in his footsteps. Fanfictions can explore how Naruto lives up to his father's reputation.