Combs began rehearsals this week in the $2.6 million revival of Lorraine Hansberry's classic play about a working-class black family.
The New York Post quoted production sources as saying Combs has agreed to take a modest weekly salary in exchange for about 20 percent of the profits.
The Post said he will earn about $1,400 a week, but could make as much as $700,000, if the show succeeds.
With those salaries, the revival can break even at below $200,000 a week at the Royale, which has a weekly gross potential of about $580,000, the newspaper noted.
"A Raisin in the Sun" opens April 26.