The experienced duo were due to be out of contract at the end of this month.
Willian featured from the start when Chelsea returned from the coronavirus-enforced break with a 2-1 victory over Aston Villa on Sunday but Pedro was an unused substitute.
Willian has made 38 appearances for Chelsea in all competitions this season, scoring seven goals.
The former Shakhtar Donetsk star is desperate to stay in London and is angling for a new three-year deal at Chelsea but the club have only offered a two-year contract to the 31-year-old.
He has been linked with moves to Manchester United and Tottenham Hotspurs.
Willian has won two Premier League titles, one League Cup, one FA Cup and the Europa League during his time in London.
Pedro has made 18 appearances in all competitions for Chelsea this season but he is likely to join AS Roma at the end of his contract.
The 2010 FIFA World Cup winner joined Chelsea from Barcelona in the summer of 2015 and has so far won the Premier League, FA Cup and Europa League.
Chelsea have eight league games remaining while they have a date with Leicester City in the FA Cup quarterfinals this weekend. The Stamford Bridge outfit still have to play the second leg of the Champions League round of 16 tie against Bayern Munich after losing the first 3-0 at home.
Chelsea are back in Premier League action against Manchester City on Thursday.
