The Serbian star is struggling to force his way into the thoughts of Blues boss Antonio Conte this season and has already been heavily linked with a move away from Stamford Bridge.
Crystal Palace and West Ham United are keen to keep him in the Premier League, but there is also interest from Italy with both Juve and AC Milan said to be keen.
Ivanovic is out of contract at the end of the season and will be available on a free transfer, but reports in Italy claim Juventus will try and strike a deal to land him in January for fear of missing.
It has been suggested Conte will be reluctant to let him leave before the end of the season as he could be needed as the Blues push for the Premier League title.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.