The 31-year-old has been a key player under new head coach Frank Lampard this season, contributing three goals and three assists in 15 appearances for the Blues in all competitions.
The Brazil international will see his contract at Stamford Bridge expire next summer, though, meaning that he would be free to agree a pre-contract with a foreign club in January.
According to Mundo Deportivo, Barca - said to be long-term admirers - want to hold talks with the South American in the hope of securing his signature ahead of next summer.
Willian has scored 55 times in 307 appearances for the Blues since arriving from Anzhi Makhachkala in 2013.
The attacker has also won two Premier League titles, one FA Cup and the Europa League during his time at Stamford Bridge.body check tags ::