The Mexican striker has been a peripheral figure at Old Trafford for some time, with new manager David Moyes appearing to have all but axed him from his first-team plans.
Despite possessing a fairly good goals to minutes ratio during his spell at the club, an end of season move is thought to appeal to all involved, which has alerted Inter.
The Serie A giants are set for a big summer in terms of transfers following their recent takeover.
Nemanja Vidic has already agreed a Bosman move to the San Siro from United, and he could be followed by Chicharito.
Inter are believed to be offering the penalty-box goal-getter regular action, which will appeal to him given his lack of playing time of late.
Hernandez joined the Red Devils in 2010 from Chivas Guadalajara in his homeland and immediately developed a reputation for his ability to find the back of the net.
But the presence of Wayne Rooney, Danny Welback and most recently Robin van Persie has seen his role diluted.