AUGUSTA, Maine — State officials think they can maximize the value of Maine’s wholesale liquor distribution business over the next 10 years, directing a greater portion of the profits to state coffers to help it pay off debt owed to hospitals and fund other priorities.

In the short term, however, the change in approach to renewing Maine’s liquor contract expands the budget hole lawmakers must fill before June 30 by $20 million.

Lawmakers this week are starting to tackle Gov. Paul LePage’s proposal for filling a $112 million gap in the current year’s budget. While cost overruns in the state’s Medicaid program are responsible for the bulk of the budget hole, a change in law proposed in the supplemental budget package accounts for $20 million of the total.

That’s because the Legislature in 2011 balanced the current two-year budget in part by including a provision that required the state negotiate a new liquor contract by June 20 of this year. The budget provision required a $20 million upfront payment to the state from the vendor awarded the new contract, in order to balance the budget. It also directed the state’s share of ongoing liquor profits to transportation and drinking water programs, state reserves and the general budget fund.

Now, the LePage administration is pursuing a different path as it looks to renegotiate its wholesale liquor distribution contract; the current contract expires June 30, 2014. The governor earlier this month laid out a plan to repay $186 million in debt the state owes its hospitals by issuing a revenue bond this year and paying it down with future profits from a renegotiated liquor contract. The $186 million in state money will trigger a $298 million match from the federal government to cover the $484 million in total debt.

LePage’s plan will soon come before Maine lawmakers in bill form. Sen. Patrick Flood of Winthrop, a Republican who wrote the 2011 budget provision that directs liquor profits to water treatment infrastructure and highways, will sponsor the governor’s proposal.

“I certainly wanted the $20 million to balance the budget” two years ago, Flood said Thursday. “If the executive branch wants to do something even wiser going forward, I would not be jealously guarding the language I put in two years ago because I’m open to better ideas.”

LePage’s bill hasn’t been printed yet, but it will propose using future liquor profits to pay down a bond the state will take out to reduce its hospital debt, then allocate the remaining funds to the same programs Flood advocated two years ago, Michael Cianchette, LePage’s chief legal counsel, said Thursday.

Maine is one of 17 states that control the distribution of hard liquor within their borders. The state leased that business to Maine Beverage Co. in 2004 for 10 years in exchange for a $125 million upfront payment and an annual cut of profits. That annual cut was $8.6 million in 2012, said Gerry Reid, director of Maine’s Bureau of Alcoholic Beverages and Lottery Operations.

If the state, rather than Maine Beverage Co., operated the liquor business in 2012 under current retail liquor prices, it would have taken in $45.9 million in profits, Reid said Thursday.

“What we’re changing is the financial arrangement so the state gets more value rather than the vendor,” Reid said.

Under a more favorable contract arrangement, the state could take in more than $30 million profit annually, according to Reid. That’s after the state pursues plans to lower some retail prices and allow liquor retailers higher profit margins in an effort to grow Maine’s spirits business.

Those lower retail prices, according to Reid, would help Maine recoup a portion of the $30 million in spirits sales the state loses annually to neighboring New Hampshire, where retail prices are generally $2- to $7-a-bottle cheaper than in Maine. The $30 million in sales amount to $11.6 million in lost profits.

If lawmakers agree to the law change the LePage administration is counting on to make the new liquor deal work, Reid said the state would issue a request for bids for a new wholesale liquor distributor later this year.

LePage on Wednesday rejected an offer from Maine Beverage Co. to help the state repay its hospital debt while guaranteeing the state at least $32 million in annual revenue in exchange for continuing to operate the business for another 10 years.

“There’s more money in this business than that,” Reid said.

Maine Beverage Co. CEO Dean Williams said Thursday in a written statement he was “disappointed” LePage rejected his company’s offer without discussing it. But, he said, “We are committed to following through on the process and hope to find a way to continue our partnership with the state.”

In the Legislature, it will be an added challenge to fill a budget hole that’s $20 million larger, said Sen. Dawn Hill, D-York, who chairs the budget-writing Appropriations Committee. But lawmakers agreed to that arrangement before the LePage administration started pursuing a different liquor distribution deal, she said Thursday.

“I just want to know it’s going to be an open, transparent process, and whatever choices are made, it’s going to be the best deal for the people of Maine,” Hill said.