Gomes is well down the pecking order at Tottenham, finding himself as third-choice keeper behind Hugo Lloris and Brad Friedel.
The 32-year-old spent the second half of last season on loan at Bundesliga outfit Hoffenheim and came close to a permanent switch to the club only for Spurs to block the move.
Gomes is keen to move on to kick-start his career as he has been frustrated with his lack of first-team opportunities at Tottenham.
The Brazilian's agent, Alex Soares, has confirmed three clubs have expressed an interest in Gomes and that he hopes Tottenham will let him leave for free this month, with his current deal due to expire in the summer.
"At the moment I have received interest from three clubs in relation to Heurelho," Soares told Sky Sports. "There is no formal offer made, it will depend on Tottenham's position.
"In my view he must leave Tottenham this month. There is no sense to keep him at Spurs if he is not playing or not even being given the opportunity to play.
"The club is paying high wages and are not using the player. They have other very good goalkeepers as well.
"I trust Tottenham will release him for free now as his contract is running out.
"Or, if they want him to stay, they must offer an extension and also give him an opportunity to fight for the No.1 position."