Besiktas defender Domagoj Vida has been closely linked with a summer exit.
Vida’s form in the World Cup has seen his valuation skyrocket with Besiktas demanding £16 million.
Turkish-Football first reported Everton expressing an interest in Vida at the start of the World Cup.
It turns out that the Toffees face competition from Leicester City.
The Foxes were reported to have made a £10.6m [€12m] bid for the Croatia international earlier this week and they have now upped that to £12.5m (€14m), Sabah have reported.
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The Toffees meanwhile have been linked with a £12m [€13m] bid for the 29-year-old.
The Merseyside based outfit have built up close ties with Besiktas following the transfer of Cenk Tosun in January.
Besiktas meanwhile have given the green light for Vida to be sold for the right price.
The Black Eagles signed the defender on a free transfer in January from Dynamo Kiev and he does have another four-years remaining on his contract.
Vida has been excelling in Russia, staring in the 2-0 win over Nigeria and 3-0 victory over Croatia.
The centre-back was rested against Iceland in the final game as Croatia had already booked a place in the next round.