Willian could agree a new deal at Chelsea before the end of the week, with the winger's current contract set to expire.
Frank Lampard has remained hopeful a deal could be struck with the former Shakhtar Donetsk forward and despite offers from a host of clubs, it appears a breakthrough has been achieved over a new contract.
Willian's agent Kia Joorabchian said in an interview on TalkSport on Tuesday the player will decide his future after the FA Cup final on Saturday.
The 31-year-old Premier League winner has been holding out for a three-year deal, while Chelsea have reportedly only offered a two-year extension.
The news will come as a blow for Arsenal, who have tracked Willian in recent weeks. Barcelona, Manchester United and David Beckham's Inter Miami have also asked to be kept informed of his availability.
Willian has played an influential role at Stamford Bridge since Premier League football returned, scoring four and assisting in three goals as Chelsea confirmed their place in next season's Champions League.
Willian missed Sunday's 2-0 victory over Wolves through injury, but hopes to be fit for this weekend's FA Cup final - after which his present contract expires.
In a post on Instagram shortly before the game, Willian wrote: "I did treatment until the last minute to be able to be in the field, but this time, unfortunately, it will not be possible.
"I will be at Stamford Bridge supporting my teammates. Come on Chelsea!"
The summer transfer window will run for 10 weeks from July 27 and close at 11pm on October 5. A domestic-only window for trades between the Premier League and EFL then runs from October 5 and closes on Friday October 16 at 5pm. Follow all the news and analysis on Sky Sports News and across Sky Sports' digital platforms.