The Turkish newspaper AMK report that the 31-year-old has agreed personal terms with his current club and will extend his deal in the coming days.
Chelsea’s vice-captain had wanted a two-year deal as his contract expires at the end of the season, however The Blues offer only one additional year to players over 30.
Ivanovic has endured a torrid campaign at Chelsea this year after helping the Blues to the Premier League title last season. The 31-year-old has been heavily criticised for his displays in defence.
AC Milan were also interested in signing the Serbian international according the the Independent.
Ivanovic – who joined Chelsea from Lokomotiv Moscow for £8.4 million back in 2008 – has made 20 appearances for Chelsea this season.
Chelsea take on Scunthorp in the FA Cup this weekend and host West Brom at Stamford Bridge in their next Premier League fixture.