Pique has also attracted the interest from Chelsea but has dispelled any rumours of a link away from the Nou Camp.
"I was really happy and left a lot of friends [in Manchester], even if I didn't play as much as I'd wanted, but I've always said I want to stay here all my career and retire at Barcelona," the 27-year-old told reporters.
"At the moment I'm not thinking about leaving. I'm really happy if it's true that United want me but I'm a Barcelona fan, I have been since I was a kid. I want to stay here."
Pique spent four years at United earlier in his career but failed to cement a first-team place, managing only 12 appearances.