Tomas Sivok's agent claims Premier League duo Everton and Fulham have expressed an interest in the Czech Republic international.
Valencia are also said to be keen, along with their Primera Liga rivals Sevilla.
Sivok's assured performances at Euro 2012 have helped to raise his profile, while the fact that he will soon be a free agent has not gone unnoticed.
His representative admits the 28-year-old now has plenty of options to consider, with it possible that he could be plying his trade in the Premier League next season.
"We have been in touch with Everton, Fulham and Valencia," Jiri Muller told isport.cz.
There is, however, still a chance that Sivok will agree to stay on at Besiktas.
His contract with the Turkish outfit is due to expire on 30th June, but they remain keen to tie him down on fresh terms.
"Besiktas are very much back in the game," added Muller.
"It will depend on the offer and Tomas' feelings.
"He wants to quietly think things over because every day there are more clubs showing an interest in his services."