A new private company or perhaps a new governmental agency could run the Illinois Lottery, and Gov. Bruce Rauner said Thursday he would be open to talk about expanding casino gambling.

Rauner, who long has complained about the revenue the state lottery has generated under a deal his Democratic predecessor, Pat Quinn, brokered in 2010, announced Thursday that the state was formally requesting bidders to take over the lottery program.

During a question-and-answer session with reporters at the Thompson Center, Rauner also said he expected the prospect of a casino in downtown Chicago would surface in discussions with legislative leaders on a “grand bargain” on the state budget.

“I’m not a fan of gaming myself. I think it . . . has negatives. That said, I’m a believer in local control. A lot of people like to gamble. It’s here,” Rauner said. “Chicago has a casino. It’s in Gary. Indiana gets the benefit. We don’t.”

“I’m open to options to expand if people want to expand. If some communities want to have it, I’m open to different options.”

Rauner said the state would move within a few months to hire a new firm to run the lottery, and that the state was looking for a contractor that can boost revenue by expanding the lottery’s online presence and better market games.

Northstar Lottery Services had a 10-year deal to manage Illinois’ lottery. Quinn worked to buy out Northstar before leaving office, a deal Rauner said his administration renegotiated to save taxpayers millions in payouts. The state says Northstar consistently failed to meet revenue forecasts.

Rauner noted there are few companies that specialize in running state lotteries, and said his administration was willing to look at companies that don’t specialize in running games. If private companies don’t come up with proposals that win over the governor, he said he would go to the Legislature to create a quasi-government agency to oversee the lottery, modeled on successful programs in other states.