The grievance hearing, according to The New York Times, will be held Feb. 26.
Members of both sides will present their cases, although the Times says it is unclear whether actor Piven will be in attendance.
A decision could be made following the meeting or additional meetings may be required. It is also possible that the two sides may pursue arbitration.
Piven left the show, which continues to play the Barrymore Theatre, citing high levels of mercury. A spokeswoman for Piven previously told Variety that although the actor wanted to continue in the production, his doctors advised him against doing so.
Tony Award winner Norbert Leo Butz succeeded Piven and played the part of Bobby Gould through Jan. 11. Academy Award nominee William H. Macy is now playing the role. Raul Esparza and Elisabeth Moss co-star. Producers of Speed-the-Plow are Jeffrey Richards, Jerry Frankel, Steve Traxler, JK Productions, Ronald Frankel, Ostar Productions, Peggy Hill, Bat-Barry Productions, Ken Davenport, Scott Delman, Ergo Entertainment, Dede Harris, Alan D. Marks, Patty Ann McKinnon, Nicholas Quinn Rosenkranz, Adam Sansiveri, Jamie deRoy and Carl Moellenberg.
Speed-the-Plow is scheduled to end its limited engagement Feb. 22.
Piven previously responded to the grievance filed by the Speed-the-Plow producers.
A statement released by Piven's publicist Jan. 16 says, "The claims made by the producers of Speed-the-Plow are absurd and outrageous. Mr. Piven's serious medical condition has been well documented by multiple physicians. He withdrew from the play due to medical necessity on the advice of his doctors, after he was hospitalized and warned by his physicians that enforced rest was necessary in order to avoid serious medical problems, including a heart attack. His symptoms included extreme fatigue, spacial problems, difficulty remembering his lines, difficulty maintaining his balance, and an alarmingly low resting heart rate. Mr. Piven followed his doctors' advice, although his forced withdrawal from the show was an enormous personal disappointment since it was a life-long dream to perform on Broadway.
"Although the producers had an opportunity to have Mr. Piven examined by their own physician, they never did so. The results of such an examination would have undoubtedly corroborated the conclusions of Mr. Piven's treating physicians and would have confirmed the medical necessity of his departure from the show.
"It is ironic that the producers have filed a grievance against Mr. Piven, since if anyone has legal claims relating to this matter, it is Mr. Piven. Among other things, the production failed to pay his required compensation and he has been defamed in the media by their false accusations."