Arbitrator Shyam Das will conduct the hearing, according to ProFootballTalk.com.
Representatives from the NFL Players Association told ESPN that they are unaware of a date being set.
The NFLPA filed the expedited grievance with the NFL on Monday to reinstate Peterson, citing "explicit language in a signed agreement" from Sept. 18, when the Minnesota Vikings star was placed on a special commissioner's exempt list after his indictment on felony child abuse in Texas.
Peterson pleaded no contest on Nov. 4 to a lesser charge of misdemeanor reckless assault, freeing him from the court system provided he fulfills the terms of his probation.
Under the collective bargaining agreement, a hearing must be held on the expedited grievance within seven days, after which an independent arbiter will render a decision within five days from that date.
The league began a review Thursday of the case under the personal conduct policy, but it said Peterson would remain on paid leave until the process is completed.
That didn't sit well with the union, which demanded in a letter to the NFL last week that Peterson be allowed to rejoin the Vikings immediately until a determination of any discipline.
"As of now, they have failed to respond or comply," the NFLPA said. "It is our obligation to protect all players' rights, and we will pursue any and all breaches of any contract between a player and his team or the NFL."
The league responded to the grievance Monday night.
"We have received the NFLPA's grievance on behalf of Adrian Peterson," the NFL said in a statement. "We have honored our commitment to Mr. Peterson and the NFLPA not to process or impose any discipline until the criminal charges pending in Texas were resolved. When Mr. Peterson decided not to contest criminal charges, we promptly advised both him and the NFLPA that we were prepared to consider what, if any, discipline should now be imposed under the personal conduct policy.
"We asked Mr. Peterson and his representatives, including the NFLPA, for relevant information. We have not received any of the requested information, but remain prepared to schedule a hearing and make a determination as quickly as possible based on as much information as available."
ESPN's Adam Schefter and Ed Werder and The Associated Press contributed to this report.
Latest On Adrian Peterson
Ed Werder discusses the latest news on the NFLPA filing a grievance with the NFL to reinstate Vikings RB Adrian Peterson.