HITC Sport understands the Seasiders have no intention of parting with the Costa Rica international.
The window of opportunity in which to make additions for MLS clubs closes on Thursday, and the Sounders were hopeful of completing a late deal.
Blackpool, though, have made it clear that they have no intention of entering into negotiations.
They snapped up Cubero last summer, bringing him in on a one-year contract that included the option for a 12-month extension.
Neil McDonald’s side have chosen to activate that clause and see the Costa Rica international as important to their plans heading forward.
He will now form part of a Blackpool side that will be looking to halt their slide at a League One level.
Bouncing back to the Championship at the first time of asking will be a big ask, but the groundwork is being put in place to make the club more secure for the future.