It is uncertain why he failed the physical, but Stork has suffered multiple concussions in his first two seasons.
The Redskins had agreed to send a conditional seventh-round pick to the Patriots in exchange for Stork on Wednesday. But, a source said, the shock of his pending release by the Patriots and subsequent trade left Stork contemplating retirement.
Stork, though, had apparently changed his mind on that stance and tweeted Saturday about looking forward to playing in Washington. That tweet has since been deleted, and he will now have to continue his career elsewhere.
ESPN 980 in Washington first reported Stork's failed physical.
A fourth-round pick in 2014, Stork started in New England's Super Bowl run two seasons ago. But a concussion and a muscle-related issue sidelined him to start 2015, though he returned to start the final seven games.
Stork has reportedly suffered four concussions in the past four years. He suffered another concussion earlier this month.
In Washington, Stork would have had a chance to compete with center Kory Lichtensteiger for the starting job at some point, a source said. The Redskins have said repeatedly this summer that they are pleased with Lichtensteiger, and they have used guard Spencer Long as the backup center. Stork would have provided more depth and options.