The Toffees are operating on a tight budget this summer.
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But former England keeper McCarthy could be available on a free transfer.
One-cap McCarthy, 33, is now one of the top earners at Southampton following James Ward-Prowse’s move to West Ham.
Despite the former Crystal Palace man having two years left on his deal, it is understood the Saints could allow him to leave for nothing in order to clear his wages.
McCarthy is now firmly second choice to Gavin Bazunu at St Mary’s.
However, he did play the final six games of the Premier League campaign last year as the club were relegated.
Everton face competition from McCarthy’s former club, Crystal Palace.
The Eagles are keen on a move after Vicente Guaita’s refusal to play for the first team as the Spaniard pushes for a move away from Selhurst Park.
Sean Dyche is having to add carefully this summer amid financial restraints.
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Youssef Chermiti was added in a £12.5million deal.
But the spending has not been big, with Arnaut Danjuma and Jack Harrison being brought in on loan.
Ashley Young, meanwhile, arrived on a free transfer following his release from Aston Villa.
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