The former Manchester United goalkeeper is currently on the books at Brighton & Hove Albion, but will see his contract expire at the end of the season.
No extension talks have been held, and that has alerted rival clubs to his potential availability.
There is still a chance that Kuszczak will end the campaign having helped Brighton into the top tier, with three points separating them from the play-off places.
The 32-year-old would appear to see his future away from the Amex Stadium, though, with his representative holding discussions about a possible step back up the league ladder this summer.
Kuszczak told sport.wp.pl: "I have given a lot to my team and brought experience from the Premier League.
"I know that I can safely play one class above.
"My agent is negotiating with several clubs, but at the moment I cannot speak about facts.
"My place is in the Premier League, I miss it."
Reports in Kuszczak's native Poland suggest that Sunderland, Fulham and Cardiff City are among those to have expressed an interest, but they are all sweating on their Premier League status.