Crystal Palace have made an £8million bid for James McCarthy but Everton want £10m for the midfielder.
The 28-year-old has one year left on contract and has been a long-term target for Palace despite a double leg fracture in January 2018.
The Republic of Ireland international has been fully fit since October but was limited to just one appearance under Marco Silva last season.
Palace manager Roy Hodgson believes McCarthy can recapture his old form and prove a shrewd addition to his squad alongside his good friend and former Wigan Athletic team-mate James McArthur.
However, Palace must improve their current offer to match Everton’s valuation.
Newcastle United manager Steve Bruce is also keen on McCarthy but Palace are in the driving seat.
Everton have signed Andre Gomes from Barcelona and Fabian Delph for £8.5m rising to £10m from Manchester City but also expect a new offer from Paris Saint-Germain for Idrissa Gana Gueye.
McCarthy though has not been offered a new contract and Everton are looking to sell now rather than allow him to go for nothing next summer.