Greenberg also happens to be the son of Hank Greenberg, who was the general manager of the Indians from 1950-59.
"Being a baseball guy, let me describe it this way," Greenberg told the AP. "We're in the bottom of the seventh inning. It's not over yet, but we can see the outcome, if we just get two innings of relief ball."
The Indians had no comment on the Associated Press report.
Dolan, whose family purchased the Indians prior to the 2000 season, has acknowledged for the past few years that he is open to adding a minority partner.
A little more than a year ago, Dolan turned to Allen & Co. for assistance in the search. Greenberg has had success with similar deals in the past. He worked with Dan Gilbert on the purchase of the NBA's Cleveland Cavaliers, and has experience with creating regional sports TV channels in New York and Chicago, among other deals.
Dolan has indicated that he has no interest in selling a majority share of the Indians.
"The franchise is very, very stable. Our ownership is stable," Dolan said at the end of August. "We have said from the outset that we, in the right circumstances, we'd look for a minority investor. The only change is a year or so ago, we actually hired somebody to help us with that process, but we're not in a hurry. When the right circumstances come along, we'll do it."
Greenberg told the AP that, in his opinion, adding a minority owner might not radically change the Indians' operating procedure in terms of player payroll.
"I wouldn't expect that, but what I do think it does, however, is broaden the base of ownership," Greenberg was quoted as saying. "If there are years where you lose a little bit of money, it's not as stressful and you don't feel the need to trim payroll in August and September or July. if you're out of the pennant race. because you're not writing the whole check."
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, follow him on Twitter @MLBastian and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.