The Manchester United skipper will be out of contract in the summer and the Serie A club is keen to discuss a deal with the Serbian, while Monaco is also interested.
The 32-year-old, who has been with the Premier League club for eight years after joining from Spartak Moscow, is out of contract in the summer with no clear signs that the Red Devils are preparing a new deal for their skipper.
Despite his advancing years, Walter Mazzarri's Inter, which are languishing down in sixth in Serie A, has lined up Vidic as a primary target as the club looks to get back on track under new owner Erick Thohir.
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Thohir is reluctant to pay more than €48,000-a-week for the defender but the Italian club remains confident that he would still be interested in the challenge of getting Inter back to the Serie A summit.
Initial talks between Inter and the Vidic camp have already taken place following a secret meeting in England, although an agreement has not yet been reached.
Further negotiations are set to take place in the coming days while Monaco is also expected to rival the Italian side for Vidic's signature, with the defender free to talk to foreign clubs having entered the final six months of his contract with United.
The veteran center back has struggled to regularly feature for David Moyes's United this season, although he has still accrued 21 appearances in all competitions despite continuous struggles with niggling injuries.
Moyes has previously hailed Vidic as the best defender with whom he has worked although the player's agent, Silvano Martina, insists that he is set to leave Old Trafford in the summer and that he would have "no trouble" in finding a new club.