The midfielder joined the club in January 2018 and made 100 appearances for the west London giants, winning the FA Cup and the Europa League.
Barkley is set to headline what could be a number of exits during what remains of the summer transfer window.
As Wesley Fofana closes in on what could become a world-record move to Stamford Bridge, Callum Hudson-Odoi is in Germany to undergo a medical ahead of a loan move to Bayern Leverkusen.
Ethan Ampadu, meanwhile, is the subject of loan interest from Serie A side Spezia, who hope to beat competition from clubs in England, Spain and Germany to sign the Wales international.
The likes of Billy Gilmour, Baba Rahman, Kenedy and Michy Batshuayi could also leave in the coming days.
Speaking on Monday ahead of Tuesday’s game at Southampton, Thomas Tuchel said: “I am very, very happy when the transfer window is over because then we have different leverage to push players and then the commitment has to be 100%, we will not accept 99%.
“The reality is that sometimes, in the last days of the window, you have to simply accept it no matter what you wish for. It’s the reality.”