ESPN's Adam Schefter reported the news, noting it's possible the 2012 league MVP returns after hitting free agency.
Peterson, 32, rushed for 448 yards and two touchdowns in six games with the Cardinals last season after coming over in a trade from the New Orleans Saints. He missed the final five weeks of the season due to a neck injury.
Josina Anderson of ESPN spoke to Peterson on Monday, with the running back saying that a Cardinals doctor told him his neck was "completely healed" and that he's "looking forward to playing next season."
While possible, a return to Arizona seems unlikely. The Cardinals only acquired Peterson after losing starter David Johnson for the season and seeing his backups flounder for weeks in his stead. Johnson is expected to return from a wrist injury when the Cardinals resume offseason activities.
Peterson, meanwhile, showed both a displeasure with and an inability to work in a timeshare in New Orleans. The former workhorse never rushed for more than 33 yards in four games with the Saints before being traded but did have a pair of 100-plus-yard games with the Cardinals when given an increased workload.
"There's no doubt Adrian still has some juice left in the tank," Cardinals general manager Steve Keim told reporters at the NFL Scouting Combine. "He still runs with a lot of anger and aggressiveness...but in today's day and age, we all know you have to be able to do a lot of different things."
Peterson has never been much of a receiving option, and at age 32, it's unclear how much "juice" he actually has left. He's missed 34 games due to injury over the last four seasons, with one stellar season interspersed with three injury-plagued campaigns.
A year ago, Peterson hung out on the market before the Saints seemingly bid against themselves to give him a two-year deal that quickly went sour. Odds are the best he can hope for this offseason is a one-year, incentive-laden contract that gives him no guarantee of being on a 53-man roster when the regular season begins.