The 29-year-old, who is out of contract in the summer after three years with the Buddies, hoped to agree to extend his career at St Mirren Park.
But Samson does not expect the club to improve the terms on offer, following discussions with St Mirren boss Danny Lennon.
Samson said: "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.
"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."