Jan Mucha's agent has met with Everton boss David Moyes over the keeper's contract which expires in the summer.
The Slovakian's representative, Jozef Tokos, told sport.aktuality.sk: "There are a number of options at the moment.
"He may reach an agreement with a new club during the season, which is legitimate according to FIFA. At the moment I cannot say more than that there are clubs interested in him. Naturally, he can make an agreement after the season as well.
"As for Everton, there is no chance an agreement will be made during the season. It is publicly known that the current manager David Moyes, announced that he would not yet sign an extension and that the club would be negotiating it only after 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."
Mucha said: "I'm glad that I've got a chance to be in goal. There have been positive reviews on my performances but I'm most satisfied about the fact that we won both league games.
"The bad FA Cup fixture will make me sorry for a long time yet but, on the other hand, it's nice to look at the Premier League table.
"We are quite high and close to the Champions League qualification spots. There are not many games left to be played in this season, so I believe we will manage to stay there."