Barcelona have offered Chelsea just over £55m for Willian.
Manchester United have also shown an interest in the Brazilian, who has been at Stamford Bridge since 2013.
Barca have had a previous approach for Willian, 29, rejected by Chelsea but have returned with an improved offer.
Guardiola hails Jorginho
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Manchester City boss Pep Guardiola has admitted he missed out on an “exceptional player” in Jorginho.
City tried to sign the Italy midfielder from Napoli but he opted for a move to Chelsea.
Jorginho played under Maurizio Sarri at Napoli and Chelsea’s new head coach was keen to be reunited with him at Stamford Bridge.
“I’m not disappointed. We tried,” Guardiola said at a press conference in Chicago – City are spending part of their pre-season campaign in the United States.
“My advice for all players is they have to go where they want to go, and in the end it would have been a mistake for him and for us if he’d decided to come here when he wanted to go with Maurizio and Chelsea.
“English football receives an exceptional player. All the best for him.”
Balcombe and Blues duo play in England U19 draw
Chelsea’s Trevoh Chalobah and Dujon Sterling (pictured) and goalkeeper Ellery Balcombe of Brentford featured again as England drew 1-1 with Ukraine at the Under-19 European Championship in Finland.
All three players also started England’s opening Group B match – a 3-2 win against Turkey – and were involved as the defending champions had to settle for a point in their second match of the tournament.
Marcus Tavernier of Middlesbrough put them ahead before Ukraine levelled shortly before half-time.
A draw against France on Monday afternoon would be enough to take England through to the semi-finals.
Defenders Chalobah and Sterling, who have been loaned to Ipswich and Coventry respectively, are among five Chelsea players in the squad, the others being defender Tariq Lamptey, midfielder Conor Gallagher and keeper Jamie Cumming, who were unused substitutes.
Jozefzoon completes move
Florian Jozefzoon has completed a £2.75m move from Brentford to Derby.
The Dutch winger has signed a three-year contract with the option of a further year.
Brentford accepted bids from both Derby and Leeds United – and the player has opted to sign for the Rams.
West London Sport recently revealed that the Bees had rejected a bid for Jozefzoon from Derby and that Leeds were also interested.
Derby subsequently had an improved offer accepted, prompting Leeds to also table a bid.
QPR trying to sign Sainsbury
QPR are looking to tie up a deal to bring in Australia centre-back Trent Sainsbury.
The R’s are hoping to sign Sainsbury, 26, from Chinese club Jiangsu Suning, possibly on an initial loan deal.
Sainsbury, whose contract expires in January, is keen to stay in Europe, having ended last season on loan at Swiss club Grasshoppers. He was previously on loan at Inter Milan.
QPR duo miss Germany trip
Grant Hall and Sean Goss have been left out of QPR’s squad for a pre-season visit to Germany.
Rangers, also without the injured Darnell Furlong, who has been sidelined by a knee injury, will play two friendlies against Hoffenheim this weekend.
Hall, who missed most of last season with a persistent knee problem and had surgery in February, has trained since the R’s squad returned for pre-season.
However, he is not yet ready to return to action and has not featured in Rangers’ four summer friendlies.
Neither has Goss, who has been struggling with a back problem.
QPR squad: Ingram, Lumley, Kakay, Baptiste, Phillips, Lynch, Leistner, Owens, Bidwell, Hamalainen, Scowen, Chair, Freeman, Luongo, Eze, Wheeler, Cousins, Manning, Smyth, Wszolek, Osayi-Samuel, Oteh, Sylla, Washington, Smith.