After AC Milan pulled out of the running to sign Tevez last week, Inter president Massimo Moratti has been in touch with the Blues to confirm they would be willing to pay 25million euros for the striker.
Although such a deal would have the significant advantage of being a straight transfer, rather than a loan, which City have consistently refused to entertain, it is understood to fall short of the club's valuation.
However, with the January transfer window not due to close for another fortnight, it is anticipated Inter will return with a further offer.
Having stated in the summer they felt Tevez was worth £40million, City, whilst accepting they are unlikely to get anything like that figure, do not want to lose out badly on the transfer fee.
It has been suggested in the past they would be willing to keep Tevez to his contract, which expires in 2014, although as the South American has been at home in Argentina for the past two months and has not played since his fateful non-appearance against Bayern Munich in September, that would appear to serve little purpose for club or player.
And, after watching his side overcome neighbours AC Milan at the San Siro last night to record a sixth successive Serie A win that leaves them just five points adrift of leaders Juventus, it seems Inter president Massimo Moratti thinks there are other potential suitors, including wealthy French outfit Paris St-Germain.
"Do we need Tevez? At this moment, it seems not, but football gives different answers every day," Moratti told Controcampo.
"The offer is there, but now we are free to decide whether to go ahead or not.
"I believe there are still other teams involved for the striker. There are clubs in England as well as PSG.
"In football there are no secrets. Our offer is 25million euros. Now it depends on them whether they accept or not."
It was another Argentinian forward who scored the decisive goal yesterday as Diego Milito's strike won the Milan derby.
Afterwards, Inter coach Claudio Ranieri was coy on his side's chances of striking a deal for Tevez.
He told Sky Sport Italia: "You never know. Do we really need him? You journalists certainly do..."
Talking to Rai Sport, Ranieri said: "If he joins he'll be very welcome."
And in his press conference, according to Inter's official website, Ranieri said: "Tevez? If the president wants to give the city of Milan a present... I'm used to working with what I've got."