The Serie A giants want to acquire the 26-year-old on a season-long loan with the option of making the move permanent for £10m next summer.
Hernandez, who is currently preparing this summer’s World Cup with Mexico, just finished his least productive season with the Red Devils, scoring just nine goals in 35 appearances. His previous low came in the 2011-12 campaign when he amassed 12 goals.
With the steady play of Wayne Rooney and Robin Van Persie, and the emergence of Danny Welbeck in United’s attack, Hernandez has fallen in the Old Trafford pecking order and has expressed a desire to become a more regular player next season.
That could hold true again with new manager Louis Van Gaal hoping to not repeat last season’s disastrous results, which saw United finish seventh in the League and without Champions League qualification next season.
Inter Milan view Hernandez as a potential partner to Rodrigo Palacio, who led Walter Mazzarri’s squad with 19 goals last season.
And Inter are also eying a move for Chelsea’s Fernando Torres, although Valencia are also interested in the Premier League duo.