Polumbus tweeted that he had a "tempting" offer to sign with the Jacksonville Jaguars, but that he couldn't leave his coaches and teammates in Washington.
Polumbus started a career-high 15 games last season. He was expected to be the backup to Jammal Brown, but Brown sat out the year with a hip injury.
The Redskins also announced that punter Sav Rocca has signed his new contract. The 39-year-old former Australian rules football player agreed to a two-year deal last week.