According to Ivaovic's representative, Vlado Borozan, City have been tracking the 24-year-old Serbian defender since last summer.
"We have an offer from Manchester City and they have been tracking Ivanovic since last summer," he told The Sun newspaper.
"We will now evaluate their bid, although the ball is still in Chelsea's court.
"However, I would not rule out Inter just yet because should a move to City fall through, I feel the lad could become an Inter player at the end of the season."
City have already bought one defender from Chelsea during the January transfer window with left-back Wayne Bridge moving to Eastlands earlier this month.