The Serbia defender announced this week he will be leaving Old Trafford after eight successful years at the club, and will seek a fresh challenge at the end of the current season.
The 32-year-old has sparked a scramble to secure his signature, with clubs all over Europe seemingly interested in the experienced centre-back.
However, Inter Milan are among the favourites to sign Vidic in the summer, and have openly expressed their desire to complete a deal.
"Vidic is an important player whose contract expires in June. Like other European clubs, we will try to get something from this great opportunity," Inter sporting director Piero Ausilio told Tuttosport.
"He is one of the players we are tracking. He has an interesting profile for Inter, as he has charisma and international experience.
"We will probably lose some players in his role because their contracts are up, so he is someone we are trying to pay attention to.
"However, it's a long way from that to saying we've already done something with regards to Vidic and I don't feel ready to confirm that."