The Daily Mirror is reporting that the La Liga leaders have been tracking the Blues man for some time and want to lure him away from Stamford Bridge this summer.
The report suggests a bid of around £12million should be enough to capture the versatile Serbian stopper, who has been regularly filling in at right-back recently.
Ivanovic was charged with violent conduct by the FA on Tuesday for punching Wigan’s Shaun Maloney in Chelsea’s victory at Stamford Bridge on Saturday.
The incident was in the build-up to Chelsea’s last-gasp winning goal and left Wigan boss Roberto Martinez fuming after the game, with Ivanovic’s opening goal also looking offside.
If found guilty, Ivanovic will be handed a three-game suspension and another defender missing will pose problems for Chelsea as John Terry is a fitness worry with a rib injury ahead of their FA Cup and Champions League semi-finals.