Anthony Gordon has reportedly indicated to Everton head coach Frank Lampard that he would like to join Chelsea this summer.
The 21-year-old has recently emerged as a target for the West Londoners, who have seen two bids rejected by the Toffees.
An initial £40m offer was allegedly turned down over the weekend before the Blues made a second bid worth £45m on Monday which was also rebuffed.
A recent report claims that Chelsea are now preparing to test Everton's resolve with a new-and-improved £50m offer for the Merseyside-born attacker.
In light of Chelsea's interest, The Mirror claims that Gordon has made it clear to Lampard that he is keen to move to Stamford Bridge before the September 1 deadline, and wants Everton to consider the next offer that they receive from the Blues.
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The report adds that the Toffees are aware that Chelsea have made informal contact with Gordon's representatives and believe the West Londoners will table a package the attacker will find difficult to turn down.
Everton are understood to have offered a new contract to Gordon last month, but the player's representatives have informed that club that he currently has no interest in extending his deal which expires in June 2025.
Both Newcastle United and Tottenham Hotspur have seen interest in Gordon snubbed by Everton earlier in the window, but Chelsea are now planning to step up their pursuit of the England Under-21 international.
New owner Todd Boehly is believed to have been impressed with Gordon's development at Goodison Park, and feels the attacker can improve further under the tutelage of Blues boss Thomas Tuchel.
Should Chelsea fail with their third bid of £50m, the Blues could be tempted to include some of their fringe players such as Armando Broja or Billy Gilmour as part of the deal.
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Chelsea are on the lookout for attacking reinforcements after allowing Romelu Lukaku to re-join Inter Milan on loan and Timo Werner to re-join RB Leipzig on a permanent deal.
A central striker is believed to be one of their primary targets in the final two weeks of the transfer window, and Gordon has featured as a false nine in Everton's opening two Premier League games of the new season against Chelsea and Aston Villa.
Gordon is primarily a winger, however, and impressed on the flanks for the Toffees last season, scoring four goals and providing three assists in 40 appearances across all tournaments.
Gordon is not the only youngster who Chelsea are targeting this summer as they are reportedly closing in on the signing of Inter Milan midfielder Cesare Casadei.
A recent report claims that the Blues have reached an agreement with Inter to sign the 19-year-old for an initial fee of €15m (£12.6m) plus €5m (£4.2m) in add-ons, with the Italian set to undergo his medical on Thursday.