Talks are at an advanced stage over a deal that will earn Vieira, the former Arsenal captain, some £150,000 a week.
Vieira said: "Nothing has been signed so far, but it is going well."
Former Inter coach Mancini, who completed an £8 million transfer to take Vieira from Juventus to the San Siro in 2006, has denied reports in Argentina that he has made a £7 million move for the former Manchester United midfielder Juan Sebastian Veron.
Vieira signed off at Inter by helping the Serie A champions to a 1-0 victory at Chievo yesterday, prompting coach Mourinho to praise his contribution at the club."I should give a special mention to Vieira, who certainly played his last game with us.
"I don't know where he will go, maybe to England which he likes a lot, but we should thank him for what he has done in these years at Inter.
"The club decided not to renew his contract, which is coming to an end, and to accept the offer of another club. I will miss him."
Emmanuel Adebayor is likely to boost City's Carling Cup hopes by returning from African Nations Cup duty with Togo on Jan 21.
With bad weather forcing the postponement of Wednesday night's semi-final first leg against Manchester United, Adebayor is now set to be available for the rearranged second leg at Old Trafford on Jan 27.