To help the East Baton Rouge Parish school system cope with a projected budget deficit in 2014-15, Aramark has offered to give the district $2 million in unrestricted funds.

That deficit increases from about $20 million to nearly $22 million if the School Board rejects the money. Aramark, which handles custodial, maintenance and other support work for the school system, is seeking in return an early extension on its contract, which is set to expire in spring 2016, though the details of such an extension were still being negotiated Tuesday.

The parish School Board is set to vote on its 2014-15 general operating budget Thursday. The budget calls for $441 million in spending but projects only $421 million in revenue, a total that includes the Aramark money. To cover the shortfall, the school system plans to dip into its almost $40 million worth of unrestricted reserves.

The board also is poised to discuss and perhaps vote Thursday on a contract extension with Aramark.

The company first took over most support work for the school system in 2004. In fall 2011, Aramark was granted a two-year extension on its contract in exchange for a $1 million unrestricted grant to the school system paid over a two-year period.

The school system is paying $26.1 million a year for Aramark’s services.

Terrance Ransfer, associate vice president of operations with Aramark, said Tuesday that his office has been talking for more than a month with school officials about ways it can help East Baton Rouge Parish save money. He described the $2 million as an “investment.”

“We’re long-term partners. We understand,” Ransfer said. “We’ve been here a long time.”

Ransfer, however, said he doesn’t know yet the precise details of any deal it will strike with the school system and may not know until Thursday.

“It’s very fluid right now,” Ransfer said. “Nothing formalized. It’s truly been informal conversations.”

Ransfer, however, acknowledged that Aramark has struck similar deals with other clients in recent years, though details differ.

“Ultimately it’s about what makes sense for the respective client,” he said.

Tarvald Smith, vice president of the School Board, said he spoke with Ransfer and said the amount of money Aramark is willing to give the school system increases the longer the extension, but he said he doesn’t know much more beyond that.

“We’re waiting on a recommendation from administration,” Smith said.

Ransfer said Aramark in Baton Rouge will have to find roughly $2 million in savings in its operations if the deal goes through. He said that will likely involve greater use of technology, but promised that service will be maintained.

“Every conversation we’ve had, it’s been clear that the level of service has to stay the same,” he said.