The Serie A giants are keen for Tevez to join them but want that initial deal to be a loan, with a commitment to buy at the end of the season.
However, City have made it clear they are not interested and would only be willing to do business over a straight transfer.
Acting Blues chief executive John MacBeath led the City delegation and was accompanied by football administration officer Brian Marwood at the talks, which took place in London.
City offered no guidance as to how the discussions had gone but it is believed the respective positions remain the same. Tevez is currently at home in Argentina and has been pictured playing golf on a number of occasions.
He has not played for the Blues since falling out with Roberto Mancini over his non-appearance in the Champions League defeat to Bayern Munich in September.
Tevez was subsequently fined for his conduct but then left Manchester and has not been back.
Although it would seem to be in everyone's best interests for Tevez to move on, Mancini outlined on Tuesday why City were refusing to countenance a loan deal.
"When Manchester City buy a player, they have to pay a lot of money," said Mancini, ahead of Wednesday night's win over Stoke, which ensured City will be top of the table on Christmas Day for the first time since 1929.
"But when we want to sell them, they have to go on loan. This is not good. It is not correct for the other players. Manchester City paid Carlos a lot of money for three years. It is correct that if one club, it could be Milan, Juventus, PSG, Inter, want him, they pay Carlos for his value. This is correct."