The agent of Olympiakos keeper Balazs Megyeri claims Everton have made an enquiry for the Hungarian.
The 22 year olds agent, Janos Hrutka, claims Everton tabled a bid for the keeper in last summer's transfer window but he preferred to stay in Greece.
"Everton made a financially good offer last summer but Balazs stayed in Athens as we thought it better for him to continue his career in Greece instead of starting a new one in England. And Olympiakos wanted him to stay too.
"Last autumn he was involved in the Greek Cup and in the Champions League but played less than before.
"At the moment there's an interest from the Premier League but fortunately his situation has improved at Olympiakos.
"Next week will be important regarding his future as Hungary have an international game which could improve his value."