The Slovakian is currently able to talk to foreign clubs over an off season move but the Toffees could still make the ‘keeper an offer.
Mucha had to wait until three weeks ago to make his Premier League debut for the Merseyside club two and half years after joining.
American Tim Howard has been the long-time number one in David Moyes’ side but recent injuries have allowed Mucha to grab his chance.
A superb individual display helped Everton to a crucial home victory over the Premier League champions Manchester City last weekend but mistakes against Wigan in the FA Cup quarter final will have affected the 30-year-olds confidence.
While Mucha is not happy about playing second fiddle at Goodison Park, his representatives have not given up hope of a new deal being signed at Everton after the season has finished.
“There are a number of options at the moment,” Mucha’s agent told sport.aktuality.sk.
“He may reach an agreement with a new club during the season, which is legitimate according to FIFA.
“As for Everton, there is no chance an agreement will be made during the season.
“I had a very useful meeting with Mr Moyes last week but at the moment I cannot reveal anything about what we discussed.”
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