Willian has reportedly turned down Chelsea's latest offer of a two-year extension.
The 31-year-old will see his current deal at Stamford Bridge expire at the end of the season.
Last month, the Brazil international suggested that he would leave the Blues this summer as the two parties were struggling to come to an agreement over a new contract.
According to UOL, Chelsea have offered Willian a two-year extension, but the experienced attacker has rejected the terms as he is holding out for three years.
The report also claims that the South American, who arrived in London from Anzhi Makhachkala in August 2013, has had approaches from clubs in the Premier League as the speculation surrounding his future continues.
Willian has again been a key player for the Blues during the 2019-20 campaign, scoring six times and registering five assists in 36 appearances in all competitions.