The clinical Mexican has been handed only four Premier League starts this season by David Moyes and is believed to be frustrated by a lack of regular football.
The 25-year-old striker has been falling in pecking order under the former Everton boss, who faces first team football competition with the likes Wayne Rooney, Robin van Persie and Danny Welbeck.
Hernandez is believed to be targeted by fellow Premier League clubs Arsenal and Tottenham as well as Inter Milan.
The Italian giants have already confirmed the signing of Hernandez's team-mate Nemanja Vidic for a free transfer.
However Inter president Erick Thohir ruled out claims that the Mexico international is close to follow Vidic's footsteps. He said: "Chicharito is a good player but we have not spoken neither with him."
Inter Milan have also been linked with Chelsea striker Fernando Torres and are keen to bolster their attacking options this summer.
Hernandez has won two Premier League titles at Manchester United but will be expected to leave the club this summer to seek regular football.
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