That would free up space and give Conte options to draft in replacements but both players could decide to stay until the end of the season, much to the frustration of the Blues boss.
Ivanovic would be able to leave on a free transfer when he falls out of contract at the end of the campaign and may wait, rather than push for a move in January.
Crystal Palace are among the clubs keen to do a deal but they may have to wait until the season is over.
Fabregas has been linked with a host of clubs including Juventus and AC Milan, while West Ham could offer him the chance to stay in the Premier League.
However, despite being frustrated with his lack of action this season, he is again ready to stay and fight for his place in Conte's side.