The Brazilian has shown that the Blues are just prepared to give him a two-year expansion as he nears the end of his current contract.
Willian has suggested he could leave Chelsea this summer because of disagreement over the terms of a possible contract extension, together with his existing deal set to expire in June.
The 31-year-old has spent the past seven decades of his career at Stamford Bridge, racking up over 300 appearances for the club across all contests.
The Blues have won four significant prizes during this period, including two Premier League titles and the Europa League, with the Brazilian frequently serving as a regular fixture in the beginning line-up.
Willian has been a prominent figure once more under Frank Lampard, contributing five goals and five assists in 34 appearances in 2019-20.
He is, however, due to become a free agent this summer and has yet to agree on new terms with Chelsea over a renewal.
Willian has revealed that he was given the opportunity to stay in west London for an additional two decades but that he is looking for three – a stance that could see him proceed if the Blues refuse to budge in discussions.
“It’s a challenging situation because Chelsea offered me two decades and they’re not going to change everything they provided. I said I needed three more years,” the winger told Esporte Interativo.
“The situation is difficult due to this. I truly don’t know whether it is going to be possible [to remain ]. My goal is to keep on working and concentrate on the rest of the season, so that Chelsea can keep on winning games.
“I have a clear mind and concentrated for the remainder of the season that we’ve left. I believe that it’s difficult [to remain ]. Let us see what happens.”
Willian was talking after Chelsea’s 3-0 home defeat against Bayern Munich from the Champions League on Tuesday night, which renders Lampard’s men facing an uphill battle to qualify for the next round.
The Blues will travel to Allianz Arena for the next leg of this last-16 tie on March 18 needing to score at least four goals against a side that have yet to lose in Europe this year.
Lampard must now pick up his players before a crucial Premier League meeting with Bournemouth in the Vitality Stadium on Saturday.
Chelsea are fourth in the top-flight standings right now, three points before fifth-placed Manchester United from the race for the final Champions League place with nine fixtures remaining.