The 29-year-old, who is regarded as one of the best shot-stoppers in Scotland, will be out of contract at the end of the season.
"The bottom line is that right now there are no negotiations. The club have made me an offer and I have been unable to accept it," Samson told Sky Sports News.
"The manager has made me aware that it was a take-it-or-leave-it-offer and, although I don't expect they will come back to me, I will remain hopeful.
"The bottom line is that I am 29 now and I need to make sure I make the right move for both myself and of course my family and their security. In respect of these two aspects I just couldn't accept the offer on the table."
A host of clubs are reportedly monitoring proceedings.