Hernandez, who has also been linked with Atletico Madrid, scored 20 goals in all competitions in his first season at Old Trafford but has since struggled to hold down a place in the starting XI, developing a reputation as a 'super-sub'.
The Mexican has never been fond of the label, however, leading to suggestions he could leave United due to the status of Robin van Persie and Wayne Rooney as the club's first-choice strike pairing.
“I know of Inter’s interest, I'm happy for this reason,” Hernandez told reporters on the Red Devils' pre-season tour of the USA, according to Corriere dello Sport.
“There are many clubs that want me, but at the moment I am a Manchester United player and it isn't respectful to talk about other teams. I don't know my future, we will see after the USA tournament.”
Former United captain Nemanja Vidic, who joined Inter upon the expiry of his contract in Manchester this summer, has expressed his admiration of Hernandez in recent weeks.