Per ESPN's John Keim, Peterson said "without a doubt" his mindset is to be the starting running back when the season begins.
"I'd be cheating myself if that wasn't my approach," the seven-time Pro Bowler added.
Washington's backfield has been decimated by injuries this preseason.
Rookie Derrius Guice is out for the season after tearing the ACL in his left knee during the Aug. 9 preseason opener against the New England Patriots. Byron Marshall is expected to miss two to four weeks with an ankle injury. Samaje Perine will miss at least one week with an ankle injury.
Former Washington quarterback Doug Williams was impressed with what he saw from Peterson's workout with the team.
"I don't know what he has left in the tank but what I saw yesterday was a lot of fuel in the tank," Williams said, via Keim.