Schildenfeld is thought to be keen on a move away from Dynamo Moscow after finding himself out of favour at the Russian club.
The 28-year-old spent last season on loan at PAOK FC and he is again hoping to fix himself up with a new club this summer.
The news has alerted a number of Premier League and Championship sides to his possible availability.
Schildenfeld is a regular in the Croatia side and played in all three of their matches at Euro 2012.
The player's UK representative, Darryl Powell, has admitted Schildenfeld is keen to play in England and that he is talking to several interested parties.
"I am talking to a number of English clubs about Gordon," Powell told Sky Sports.
"Gordon is keen to play in England and he would be a great signing for someone as he is a top quality central defender with a wealth of experience."