Klaff could not be reached. He is president of a privately held Chicago real estate investment company focused on acquiring U.S. office and distressed retail space.
Also approved, but teaming up with Tokarz, is a group led by New York City taxi tycoon Andrew Murstein, said a third source, who also requested anonymity.
The Tokarz group includes private equity investor and Republican operative Fred Malek, who previously bid on the Washington baseball team and was once part owner of the Texas Rangers club.
Murstein's group—Sports Properties Acquisition—includes former home run king Henry Aaron and Jack Kemp, a former U.S. congressman and star quarterback in the National Football League.
Cuban is also the owner of the Dallas Mavericks National Basketball Association team.
Tribune, which owns the Chicago Tribune and Los Angeles Times newspapers, is selling the Cubs and the other assets to cut debt it took on when it went private in an $8.2 billion deal led by real estate magnate Sam Zell.
Tribune plans to keep a 5 percent stake in the team in a deal that could save the company millions of dollars in taxes, a source previously told Reuters.
A Tribune spokesman said the company would not comment on the sales process other than to say officials are focused on maximizing the return.
Bidders are anxious to take control of the team, which is in first place in its division and in contention for its first World Series title since 1908. The Cubs are nationally recognized due to their history as lovable losers and their national exposure on cable television.
The remaining bidding groups will see the Cubs' detailed financial data next and then receive a management presentation before final bids are accepted and a winner selected, probably after the baseball season ends.
A deal could be finalized by year-end or early next year, pending approval by Major League Baseball.
Among those eliminated from the bidding were John Canning Jr., chairman of Chicago private equity firm Madison Dearborn Partners and an early favorite to win the bidding because of his close ties to baseball commissioner Bud Selig.
Other unsuccessful bidders were Don Levin, owner of the Chicago Wolves minor league hockey team; a group that had been led by Rocco Landesman, who heads a company that owns several Broadway theaters; and a group of unidentified private equity investors, according to sources.
In addition, the Chicago Tribune has reported that three groups are bidding just for Wrigley Field, which Zell previously tried to sell to the state of Illinois. Offers for that asset ranged from $250 million to $400 million, a source previously said.