The versatile international full-back has started one league game this season, but is very much on the fringes of the squad under David Moyes.
Fabio spent last season on loan at Queens Park Rangers and he admits that the time for him to leave the club is fast approaching.
"I don't know [about my future]. I think the time has come and maybe in the next window or even next season, I think I might leave," he is quoted by ESPN Brasil.
"There are good possibilities. I'm looking for other clubs. There's nothing certain, we'll leave it for later.
"I want to be happy. I want to play, I want to be with my family. I can return to Brazil, or maybe not, I'm checking with my agent to see what is the best for me."
Fabio admits that returning to his homeland is a real possibility. Both he and twin Rafael left Fluminense for United, before they played first-team football.
"I have a very big affection for Fluminense," he said.
"I played there for seven years, and certainly if I have to go back to Fluminense I would go with great pride, because I have a special affection for them."