The Brazilian playmaker, who is Chelsea's third longest serving player, is out of contract at the end of the season and will be able to walk away on a free transfer unless the Blues can get him tied down to a new deal.
Chelsea boss Frank Lampard has expressed a desire to secure the player's future, but as things stand there is no sign of him putting pen-to-paper, and that could open the door for rival clubs to swoop in.
Both Barca and Juve are said to be keeping an eye on developments as they could open talks with Willian's representatives in January with a view to hammering out a pre-contract agreement for the summer.
Willian is sure to be tempted by the prospect of a move to either club. At the age of 31, it could be his last chance for one final big move.