Tevez, who is currently pondering his options on holiday in Argentina, had appeared most likey to either stay with Manchester United or join Manchester City. However, the firm interest of Chelsea would represent a viable option away from United yet still provide the lure of Champions League football.
Tevez has been hugely disappointed by the time it took United to formally offer a deal to make permanent his two-year loan spell.
An offer is now on the table from United, which would see the Premier League champions pay a fee of £25.5 million to Tevez's investors, although the 25-year-old does also have the option of better personal terms at City. He previously spent a season in London with West Ham, but it is understood that he would now prefer to remain in the North West.
Despite the interest from Chelsea, City remain determined to make Tevez their second major signing of the summer following the £12 million deal for Gareth Barry.
Chelsea are likely to make significant changes to their squad this summer, with Ricardo Carvalho and Deco expected to join former manager Jose Mourinho at Inter Milan.
Mourinho worked with both players at Porto and Carvalho was one of his first signings when he joined Chelsea in 2004.
Inter owner Massimo Moratti said he had opened negotiations with Chelsea at Mourinho's request, while Carvalho made it clear on Monday night that he hoped to leave.
He said: "I believe my time at Chelsea is reaching an end. I am happy such a big club as Inter is interested in me and ideally I will leave this year. Being able to work with Mourinho again is very important to me."