A £115,000-a-week four-year contract is on the table for the centre-half and City will make their bid in the next few days.
Vidic, 28, has been unsettled for some time - but will not make any official announcement about his future until Serbia are out of the World Cup.
Paolo Fabbri, an associate of his agent Silvano Martina, confirmed Vidic could quit Old Trafford.
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."
Landing Vidic would represent a massive coup for City chief Roberto Mancini and a huge blow for Alex Ferguson.
The United boss has shown interest in £10m Palermo centre-half Simon Kjaer and he is seen as a possible replacement for Vidic.
Danish international Kjaer is regarded as one of the top defenders in Serie A.
bet u my balls he wun go there :) Now EPL we have 6 or 7 good teams fighting for 4th place. Man city may not even make it. Players will consider this for sure.
but the £115,000-a-week contract is tempting
wa, up levels.
last time was "agent" always spread rumour. now associate of agent also can liao.
Would he swop Champions League football for Europa League football? I think not.
City too desperate already.
This doesn't make sense. It's his wife who can't get used to life in England, and it's her unhappiness that is the source of all the rumours about him wanting a move to Spain or Italy.
If he really were to move across town and continue staying in Manchester, his wife would still be unhappy.
Real Madrid are closing in on a £30million deal for Nemanja Vidic, while Sunderland are after Matthew Upson and Man City want Philippe Mexes.
Manchester United are hoping to sign Germany captain Michael Ballack.
Talks over Manchester United striker Wayne Rooney's new contract have been delayed.
Manchester United want to loan out striker Mame Biram Diouf next season.
As reported by Spanish sports daily AS, English press sources have claimed that Real Madrid could make a summer transfer swoop for Manchester United central defender Nemanja Vidic and could include French striker Karim Benzema to sweeten the deal for the Red Devils.
The Serbian reportedly does not have very good relations with United manager Sir Alex Ferguson and with Jose Mourinho watching the central defender intently, Los Blancos could look to bolster their central midfield during the summer with the highly-rated defender.
But United will not part with Vidic for less than market value and with Sir Alex having an eye for rising French star Benzema, a mutually beneficial deal could be in the works for the two teams. At United, Benzema would serve as Wayne Rooney's strike partner.
Benzema has been disgruntled during his first year in the Spanish capital. After a €30 million -plus transfer to Los Blancos.