Everton have reportedly offered Besiktas €15 million in a deal to sign Domagoj Vida this summer.
According to T24, the Toffees are looking to step up their interest after it was revealed that local rivals Liverpool are not in the running to sign the Croatian defender.
Previous reports had suggested that both Liverpool and Everton were interested in signing the player who has impressed at the World Cup in Russia.
The defender’s performances in Russia have sparked interest from a host of clubs in Europe, but the Turkish side are reportedly holding out for a fee closer to €30 million.
Vida is set to play against England on Wednesday night for a place in the World Cup final.
There had been some suggestions that he would be banned by FIFA for the game after he was filmed dedicating the victory to Ukraine following conflict between both Croatia and Russia.