The midfielder has been linked with big names in the Premier League.
Fanatik are reporting that Manchester United, Liverpool and Tottenham Hotspur are all keen on the player – but that he prefers a potential move to Everton where he could work with new boss Ronald Koeman.
First team football would also be more of a guarantee at Goodison Park if he were to make a move to the Premier League.
Tufan, who has 27 caps for the Turkish national team, is currently contracted to Fenerbahce and has become well known for his swashbuckling and versatile approach – although his best position is undoubtedly in central midfield.
Everton Chairman Bill Kenwright and new manager Ronald Koeman pose
Everton are looking to improve their playing squad this summer after a disappointing 2015-16 campaign which saw Roberto Martinez get the chop and Koeman come in to replace him.
So far the club have brought in goalkeeper Maarten Stekelenburg and a clutch of young players this summer and Evertonians are still craving a bigger name acquisition before the season gets under way.
Tufan might just be one potential incoming.