Willian's current deal expires in June and it's understood that he's very unlikely to renew his contract, as he looks for a change of scenery.
According to Marca, Barcelona have taken advantage of the stall in negotiations and are close to wrapping up a pre-contract agreement with the Brazilian.
Willian has been at Chelsea since 2013, when he joined from Russian outfit Anzhi Makhachkala - notoriously snubbing Tottenham Hotspur at the last minute.
Frank Lampard has utilised Willian as an experienced head amongst a squad lined with young players.
The wide man may prove pivotal in the second half of the season following Chelsea's failure to make any new additions in the January window.
The bids culminated in an offer that was believed to worth about £55m, which Chelsea rejected.
La Blaugrana ended up signing Willian's fellow countryman Malcolm from Bordeaux instead, who has since moved to Zenit St. Petersburg.
Suarez,33, is thought to be out of action until the end of the season - Antoine Griezmann has been struggling to fill the gap thus far.
