The 24-year-old is a target for Chelsea as they seek to replace Thibaut Courtois after Spanish media reports claimed Real Madrid lodged a bid with Chelsea for the Belgian.
Pickford impressed during the 2018 World Cup finals as England finished fourth, following his first season on Merseyside. He cost the Toffees £30m from Sunderland in one of last summer’s surprise moves.
The Washington-born goalkeeper has four years left on his current deal, but the Everton hierarchy are keen to fend off their more illustrious Premier League rivals by ensuring Pickford’s wages stand comparison to any on offer in the top-flight.
He returns to pre-season training this week after a brief holiday following England’s third-place final defeat to Belgium a fortnight ago.
Pickford was a pivotal player in the tournament run enjoyed by Gareth Southgate’s men. It included England’s first World Cup penalty shootout win in which the Everton keeper saved Carlos Bacca’s penalty to set up the victory.
It will be the first time he works with new Toffees boss Marco Silva and his coaching staff ahead of Everton’s opening Premier League match of the season against Wolverhampton Wanderers.