Tuttosport reports that Juventus are eager to bring Vidic to Turin in the same way they snapped up Andrea Pirlo from AC Milan in 2011.
The Manchester United defender is out of contract at the end of the season, and his agent has suggested he could move on in the summer.
Vidic has struggled with injury over the past two seasons, and with Phil Jones, Jonny Evans and Chris Smalling pushing for regular first-team spots, David Moyes could let him leave.
Pirlo left Milan after the player and club reached a mutual decision not to renew his contract. Despite the fact that many felt Pirlo's best days were behind him, he signed a three-year deal with Juve and was this year named the fifth best footballer in Europe by Bloomberg at the age of 34.
That followed a starring role at Euro 2012 as Italy reached the final.
And the report claims Juventus hope to pull off a similarly savvy agreement to sign up the 32-year-old Vidic.
The Serbian's performances have dipped from his own high standards this term, but Juve want to take the low-risk financial gamble on his future fitness and form.
He reportedly shares an agent with Gianluigi Buffon, and despite interest from Fiorentina and Napoli, the report claims Juventus chief Giuseppe Marotta is also keeping a close eye on developments.