Besiktas defender Domagoj Vida has been closely linked with a summer exit over recent weeks.
Turkish-Football first reported Everton interest in Vida last week.
Besiktas are prepared to sell Vida but only once the World Cup is over, hoping his value will keep on rising.
Sports newspaper Fanatik went onto report that the Toffees made a €13.2 million offer for the centre-back.
Per the source, West Ham are also in the race for the Croatia international.
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Leicester City were then reported to have made a €12m move according to
Vida has opened up about the latest transfer reports and revealed that he will make a final decision over his future after the World Cup.
“All I am focused on right now is the World Cup, I will make a decision regarding my future one the tournament is over. After Russia I will take a look at the offers,” Vida said.
The 29-year-old has been in great form for Croatia, helping his side keep clean sheets in the 2-0 win over Nigeria and the 3-0 victory over Argentina.
Croatia have already booked a place in the next round after winning their opening two games.
Vida joined Besiktas on a free transfer from Dynamo Kiev in January and has another four-years remaining on his contract.