Tevez is reported to have said he will return to Manchester on Tuesday after spending the last few months back home in Argentina following his row with Mancini during a Champions League tie against Bayern Munich in September.
The Argentina forward has not played for City since he refused to warm up during the Bayern defeat and he was expected to leave the Premier League club during the January transfer window.
However, City were unable to agree a deal with AC Milan, Inter Milan and Paris Saint Germain and Tevez has now indicated he is ready to resume his career with City.
Mancini, who saw his side return to the top of the table with a 1-0 win over Aston Villa on Sunday, had previously insisted Tevez would never play for him again, but he now appears to have softened his stance.
"My reaction is always the same. Carlos knows the situation, we are here and it depends on him," Mancini told Sky Sports.
"Carlos knows the situation from September, we don't have any problem."
Asked if an apology was still what City were waiting for, the Italian added: "Yes, it's possible. For Carlos' situation, we know what can happen.
"Carlos is a Manchester City player. We are in Manchester, we are always there. We have not changed in these three months, we are there."