The defender has been linked with a move away since it was announced that Jose Mourinho was returning to the club, and Barca have been keeping an eye on his situation.
Mourinho is planning to bring in defensive reinforcements before the transfer window closes, but Ivanovic remains in his plans as the player's versatility could prove to be crucial throughout the season.
The Serbian is now 29 and would like to see out his playing days at Stamford Bridge, and is targeting a new deal.
"All being well, Branislav would like to be a Chelsea player for the remainder of his playing days at the highest level," a source close to the player has been quoted as saying.
"He is definitely staying at Chelsea. He loves Mourinho's style and is keen to play for the new coach.
"He has been told that he does have a future at the club and, while there was the possibility of him going to Barcelona, he is happier staying in London."