There is increasing confidence in Albany that much — though probably not all — of the state school aid forfeited by the city earlier this year will be restored when a final budget is submitted.

Whether any aid would be restored seemed less likely a week ago. Several key New York City Democrats didn’t immediately support the cause and the Bloomberg administration was not actively lobbying for it.

But that changed this week, as negotiations to adopt a $136.5 billion budget got underway. The city ramped up its presence in Albany, and State Sen. Diane Savino, whose support has been courted by other Democrats, said today she was more optimistic that some funding would be restored.

“There’s going to be a solution … that’s not going to overly punish New York City children,” said Savino, a Staten Island Democrat whose breakaway caucus controls the Senate along with Republicans. A source close to negotiations said that “at least some” of the $240 million lost by the city this year would be restored.

Earlier this week, the Bloomberg administration circulated a memo listing state aid restoration as a top budget priority. Chancellor Dennis Walcott personally reinforced that request on Wednesday when he went to Albany to discuss the city education department’s priorities with lawmakers.

In addition to getting the aid restored, the city is asking for more transportation aid during emergencies and natural disasters; control over preschool special education tuition rates; and the rejection of a proposal to require busing for students in school after 4 p.m. (The memo is below.)

Most of the legislature’s negotiations over the weekend will focus on school aid in New York City, which missed a mandated teacher evaluation deadline earlier this year. How much will be restored remains the big question up for debate in the final days of budget talks. Lawmakers hope to reach a budget deal by Monday to allow a budget law to be passed by the end of the week.

Lawmakers from the Education Conference Committee are figuring out how to split up an extra $290 million, a pot of funds known at a “table target” that is available on top of Gov. Andrew Cuomo’s spending plan.

Assemblywoman Catherine Nolan wants to use as much of the funds on New York City as possible. But Republican lawmakers from outside of the city have made it clear they want the money spent on their own school districts. In Long Island, there is a push to restore “high tax” aid, a form of school funding for districts that have been especially hit by the cap on property taxes.  Cuomo’s budget cut aid by $50 million.

Cuomo has already made one concession on state aid for New York City. He agreed to put money back into the city’s base funding for future years, ensuring that there won’t be a $240 million deficit in future years as well.

“Getting it put back into the base, that was huge because then we don’t have the compounding effect for years and years and years,” United Federation of Teachers President Michael Mulgrew said this week.

Assembly Speaker Sheldon Silver and Nolan agreed, but they both said the adjustment didn’t go far enough. They said they’d continue to fight for restoring the lost aid for this year, too.

New York City’s 2013-2014 state budget priorities — Education