According to ESPN sources, the Belgian global who returned to training on Monday has told the former Napoli manager that he wants to quit Stamford Bridge as there is only one year left on his contract.
Chelsea lost the Community Shield 2-0 to Man City on Sunday, with numerous Blues' side looking out of sorts.
The Premier League club are thought to be willing to let him leave, providing they can find a replacement, while Maurizio Sarri said yesterday that he didn't want to keep him at the club if he wasn't fully motivated.
Barkley, 24, endured a torrid start to life at Stamford Bridge last season as a combination of injury and poor form restricted him to just two Premier League appearances following his January arrival from Everton.More news: South Sudan rivals to sign final power-sharing deal in Khartoum
Chelsea will, however, be encouraged by the timely return of Hazard and Kante, the pair having been linked with Madrid and Paris Saint-Germain respectively.
Manchester City's pursuit of Jorginho faltered because Chelsea had a more pressing need for the Italy midfielder.
"I'm a Chelsea player".
The wide man said: "I was always clear about wanting to stay here". I've watched clips of his Napoli team to see the way they played. "I'm joking. I think Conte was, for me particularly, a manager that was hard to work with". The other clubs that compete with us are really strong and already have fantastic teams and squads, like Chelsea, Tottenham, Manchester City, or they are investing massively like, for example, Liverpool, that is buying everything and everybody.
After a series of events, the spotlight is yet again back on Courtois transfer saga as the player's agent Christophe Henrotay has called on the London club to allow his client to move to Bernabeu, various reports acknowledge.