Keane spent the back end of last season on loan at Wednesday, and his showings impressed Stuart Gray.
The Owls boss is now hoping to re-sign the 22-year-old, who he believes could be the man to lead Wednesday's attacking line next season.
The Yorkshire club struggled for goals last term and the signing of a striker has become a top priority for Wednesday this summer.
The Owls have money to spend following the takeover of Dejphon Chansiri, and Gray reportedly feels that adding a clinical goalscorer is the most pressing concern for the club.
It means that Keane has become an obvious target and United could well listen to offers for the striker, who still seems some way down the pecking order at Old Trafford.
While on loan with Wednesday, Keane made 13 appearances and managed to score three goals during that period.