Despite City's continued interest in signing Napoli striker Edinson Cavani, it is understood that new manager Manuel Pellegrini would like to retain Tevez at the Etihad Stadium.
City are also believed to be interested in signing the Portuguese international defender Pepe, who has been told that he can leave Real Madrid this summer, even if the club are publicly insisting he is not for sale.
Incoming Real coach Carlo Ancelotti is prepared for Pepe to go if a fee of about £20m can be agreed but City will not want to pay that much for a 30-year-old. Pepe fell out with previous coach Jose Mourinho after losing his place to Raphael Varane, who will remain first-choice next season.
Talks are planned over Tevez's future at the Etihad Stadium, with the 29-year-old having just 12 months left on his present deal.
If Tevez does leave City this summer, he does not want to remain in the Premier League, despite suggestions that there could be interest in him from Liverpool or Chelsea. Tevez would eventually like to end his career at Boca Juniors, his first club in Argentina.
City are pressing ahead with their plans to reshape the first-team squad with Pellegrini poised to be confirmed as manager as early as tomorrow, succeeding Roberto Mancini.
The Chilean is an admirer of Tevez and it is understood that he is keen to retain him along with fellow Argentinean Sergio Aguero.
The future of Edin Dzeko is far less certain with City willing to listen to offers for the Bosnian striker. Dzeko is interesting Chelsea – having previously drawn interest from Tottenham Hotspur – and has also been discussed as a possible makeweight in the deal to bring Cavani from Napoli.
City are acting quickly to strengthen their squad this summer with Brazilian midfielder Fernandinho having completed his £34m move from Shakhtar Donetsk. The 28-year-old will soon be joined by Seville winger Jesus Navas for an initial £14.9m.
City also have to hold talks with England internationals Joleon Lescott and Gareth Barry who, like Tevez, have only a year left on their present contracts. With Fernandinho signing, Barry's future at City would appear to be in some doubt while defender Lescott lost his place last season to Matija Nastasic.