The Everton and England goalkeeper faces an uncertain future in the coming months.
While the Toffees have avoided relegation, administration is still a possibility for the club.
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Per talkSPORT, a big enough offer may mean that Everton have no choice but to sell.
Chelsea are the team that the source believes is most interested in signing Pickford.
While the Blues signed Djordje Petrovic and Robert Sanchez last summer, they are not impressed by either.