Everton boss Ronald Koeman says he cannot guarantee that Romelu Lukaku will be part of the Toffees squad when the transfer window shuts at the end of the month.
Chelsea are interested in signing the Belgium striker and are willing to offer Everton £60m ($78m) and Loic Remy for his services, according to the Evening Standard.
The paper says Lukaku is desperate to return to Stamford Bridge and is considering handing in a transfer request to force through a move.
Earlier reports suggested that Everton were reluctant to sell the 23-year-old and were holding out for a fee of £75m.
The Merseyside club are flush with cash after selling John Stones to Manchester City for £47.5m and are under no pressure to sell a player who has three years left on his contract.
"He is still an Everton player but the board makes those kinds of decisions," Koeman was quoted as saying by the Evening Standard.
"Of course, I would like to keep all my best players but I know football. I know business. Let's wait.
"The club is doing everything to keep all the players we'd like to keep in the team."
Lukaku made 10 league appearances for Chelsea between 2011 and 2013 before being loaned out to Everton at the start of the 2013/14 season.
He joined the Toffees on a permanent basis a year later after Everton agreed to pay a £28m transfer fee.
The striker is doubtful to play in Everton's opening Premier League fixture against Tottenham on 13 August due to a foot injury suffered in a pre-season friendly against Espanyol.
"Romelu Lukaku is doubtful for the weekend because of the cut he got against Espanyol," Koeman was reported as saying by Everton's official website.
"We also have Seamus Coleman doubtful with an ankle injury."