"I am sure they (the club) are speaking to Mark," Davies said. "There is no doubting his ability and what he has done for the club. It is a no-brainer about trying to keep him, and I hope he stays."
Schwarzer was heavily linked with a dream move to Arsenal during the European summer but nothing eventuated.
He is now hoping to get a transfer away from Fulham to a club involved in the Champions League so he can play at the top European level before his career ends.