The Greenway Conservancy is pitching a beer garden for its downtown grounds as a “hip,” “offbeat” moneymaker — but the nonprofit won’t say what cash the hops will generate as calls to wean itself off state funding intensify.

The Greenway’s $2 million-a-year state subsidy is set to expire July 1, and the state, the conservancy and park abutters are in talks that could bring a new funding arrangement.

The nonprofit behind the 17-acre Rose Fitzgerald Kennedy Greenway is giving a handful of interested operators until Friday to submit final proposals for the 5,000-square-foot “biergarten/wine bar” envisioned for the corner of Purchase and High streets.

The winning bidder would be responsible for upfront investment, operating costs, and the facilities for a beer garden that runs three to five nights a week during warm-weather months. The conservancy meanwhile, is eyeing both monthly payments and a cut of gross revenues as part of a one-year “revenue-sharing agreement,” according to a request for proposals.

But conservancy officials, citing the ongoing process, could not say how much they hope to earn off the project, which comes as they’re hunting for other revenues.

“Doing a beer garden is not in reaction to other funding,” said Jesse Brackenbury, the conservancy’s executive director. “The reason we do this is because it’s a great amenity for the public. It will also earn income. We will see what it might earn us in year one. From that, there’s a possibility for growth over time. That’s why we were doing this.”

Greg Sullivan, a former state inspector general now at the right-leaning Pioneer Institute, praised the idea of a beer garden as a sign the conservancy is looking for other ways to be fiscally nimble and draw in more visitors. But it shouldn’t stop there, he said.

“I think they should be thinking about other things that would fit for the Rose Kennedy Greenway to be an attractive place for people to visit,” he said.

“There’s been a wide belt between the promises of funding and fundraising, and reality.”

Brackenbury said talks with the state are still ongoing, adding that he’s “confident in a shared resolution.” But he defended the conservancy’s ability to draw in other revenue, which includes $959,000 in its own earned income last fiscal year. It took in just $69,000 in 2010.

The jump has been buoyed by the success of its food truck program, which now makes the nonprofit roughly half-a-million dollars a year, compared to $30,000 when it started. But Brackenbury acknowledged, “I don’t see that kind of trajectory for a beer garden.”

The nonprofit has come under fire in the past for its spending habits and hefty salaries as the state funds about 40 percent of its $5.1 million budget. Gov. Charlie Baker said last year that he expected the nonprofit to pull itself off state funding in the “not too distant future,” and the potential has prompted calls for others, from the city to neighbors to businesses, to put more toward upkeep for the park.

“I think that the idea of generating more revenue is certainly something that the Greenway should explore,” said state Rep. Aaron Michlewitz, a North End Democrat whose district includes the Greenway. “The funding mechanism that currently exists is not conducive to long-term success. And we need to think of a different operation.”