City are ready to offer the Serbian defender a £115,000-a-week four-year contract, according to The Sun.
City will make their bid in the next few days.
Vidic’s agent has hinted that his client could leave Old Trafford this summer.
Silvano Fabbri said: “We are waiting for Nemanja to tell us what we he wants to do. Any eventual transfer will take place only after the World Cup.”