Bernard has been linked with a potential exit from Goodison Park in this month’s transfer window, with Serie A giants Roma floated as a possible destination.
However, the winger also has interest from the Middle East, where Dubai-based outfit Al Nasr are keen.
Al Nasr want to sign the Brazilian winger on a permanent deal before this month’s transfer window slams shut.
The United Arab Emirates side are claimed to be considering putting in a bid of around £10m in an effort to secure Bernard’s services.
The wide-man has struggled to nail down a spot in the Everton team under Carlo Ancelotti and has another 18 months left on his contract on Merseyside.
Al Nasr currently have two Brazilian players on the books in the shape of defender Glauber and striker Caique.
The club currently sit in fourth spot in the United Arab Emirates top flight.