According to Ian Rapoport of NFL Network, Washington is hosting Peterson for a team visit.
Josina Anderson of ESPN also noted the player's interest in joining the Redskins.
"I'm down for working out or whatever I have to do to make the team," he said Sunday.
The 33-year-old averaged just 3.4 yards per carry after producing only 1.9 yards per carry in his three games in 2016.
Still, Peterson is only a few years removed from leading the NFL with 1,485 rushing yards and 11 touchdowns in 2015 with the Minnesota Vikings. That season marked his fourth All-Pro and seventh Pro Bowl selections as part of his likely Hall of Fame career.
He has, however, struggled to find a landing spot this year.
Washington is in need of backfield help after rookie second-round pick Derrius Guice tore his ACL in the team's first preseason game.
Samaje Perine suffered a sprained ankle and will likely miss at least a week, per Mike Garafolo of NFL Network. Byron Marshall will likely miss two to four weeks with an ankle injury, per Tom Pelissero of NFL Network.
And with Chris Thompson still recovering from a broken fibula, Rob Kelley is the only healthy and established running back on the roster.