The French midfielder's current deal at Bloomfield Road is due to expire at the end of the current campaign, meaning that he would be available for a free transfer unless an agreement over fresh terms is reached.
However, Sylvestre's claim has suggested that the Seasiders are hoping that they can keep hold of the 29-year-old.
"The club spoke to me last week. I have to sit down with my agent and see what's going to happen," he said.
"I don't know if any other clubs are after me, I just let my agent sort it all out. I need to talk to the gaffer and chairman and we'll see what happens."
Sylvestre joined Blackpool from Mlada Boleslav in 2010.