Swansea City have set an asking price of £50m for midfielder Gylfi Sigurdsson after rejecting an offer worth around £40m from Leicester.
Sigurdsson, 27, scored nine goals and made 13 assists to help save the Welsh club from relegation last season.
Everton have long been interested in the Iceland playmaker, who said in May he was “not trying to leave” the Swans.
With the Toffees reportedly demanding £50m for Ross Barkley, Swansea would want the same for Sigurdsson.
Sigurdsson has three years left on his contract, which he signed last year to become Swansea’s highest paid player.
He has scored 30 goals for the club since rejoining them in 2014 after an indifferent two-year spell at Tottenham.
Sigurdsson is settled and happy to stay at the Liberty Stadium, though Everton could test the Swans’ resolve with a significant offer.
Everton have enjoyed a productive transfer window, re-signing Wayne Rooney from Manchester United and spending a potential £30m each on centre-back Michael Keane and goalkeeper Jordan Pickford.
They have also signed midfielder Davy Klaassen for £23.6m and striker Sandro Ramirez for £5.2m.
But with Toffees striker Romelu Lukaku set to join Manchester United for an initial £75m, the Merseyside club could still have the funds to finance a move for Sigurdsson.