Sigma Olomouc have told Hamilton that they will need to pay 200,00 euros (£178,000) if they want to sign Tomas Cerny.
The goalkeeper has impressed during his loan spell in Scotland, but that is due to come to an end this summer.
Old firm giants Rangers and Celtic are both said to be showing an interest in Cerny and Olomouc have warned Hamilton they are ready to talk to other clubs if the SPL side do not pay before the end of May.
"If Hamilton don't pay 200,000 euros, then we will start negotiations over Cerny's future ourselves," director Jiri Kubicek told Deniksport.
"And we can discuss it with both Rangers and Celtic, if they contact us. So far this has not happened."
Hamilton boss Billy Reid insists he is determined to keep Cerny.
"It doesn't surprise me that Tomas is attracting attention," Reid told The Evening Times.
"He has been outstanding for us both over the course of the SPL season and during the latter stages of our First Division title-winning season last term.
"Obviously we want to keep Tomas and, in that respect, we are certain he will still be a Hamilton player next season.
"We know exactly what the situation is with Sigma and that does not alter the fact we are confident of keeping Tomas at New Douglas Park next season."