The 31-year-old is currently due to leave the club at the end of this month when his existing deal comes to an end, having failed to agree terms over an extension with the Blues.
Willian remains keen to stay at Stamford Bridge but has been holding out for a three-year contract, whereas Chelsea have only been willing to offer two years.
However, Sky Sports News claims that they have now been able to make progress in talks and that Chelsea are now confident of keeping the Brazilian attacker.
Willian had been linked with moves to the likes of Arsenal and Tottenham Hotspur after revealing his preference to stay in London, while Barcelona, Manchester United and Inter Miami have also reportedly asked to be kept up to date with any developments.
The winger has scored 11 goals and created nine more in 47 appearances across all competitions this season.