The Daily Mail says Boca - Tevezâ€™s first professional club - have little hope of raising a transfer fee that would be acceptable to Manchester City, but are encouraged by the 27-year-oldâ€™s desire to be closer to his daughters in South America.
Boca vice-president Juan Carlos Crespi said: "I want to see Tevez play for Boca. There is good chance."
The striker, who will return to Argentina this week, has often said he would like to return to Boca before the end of his career but admits a move now would be difficult.
"To go back to Boca Juniors would be beautiful but it is very difficult," he said last week.
"I spoke to (Boca midfielder Juan) Roman Riquelme and, messing around, we agreed I would go back one day. But if weâ€™re speaking seriously, financial issues would make my return difficult."