The cost to convert the vacant Woolworth building on Public Square into rental housing could jump from a projected $7.275 million to between $10 million and $12 million.

New partner David Gallo and two of his Long Island partners, Anthony and Matthew L. Ardito, gave the Watertown City Council an update on the project during a work session Monday night.

Mr. Gallo stressed he won’t have more accurate details on its cost until the project proceeds. He also could not predict when work would start on the landmark. He and his partners — including Long Island developer Michael A. Treanor, who has been involved in building renovations in Jefferson County — continue to work on obtaining state and other financing for the project, Mr. Gallo said.

“There are a lot of variables we cannot necessarily control,” he said after the meeting.

City officials and the developers agreed the discussion opens the dialogue between them. Mr. Gallo promised to give them more updates and details in the future on how the project moves ahead.

Meanwhile, council members made no decision on whether the city will give up the adjacent site of the CitiBus transfer station and some green space across the street for parking for the building. Parking may be a sticking point for the project to proceed.

“This is the first inning of a nine-inning game,” Councilman Joseph M. Butler Jr. said later.

Council members also learned the number of apartments also has been reduced from 60 to between 45 and 50 and would contain a mixture of market-rate units and affordable housing. Retail shops would be on the ground floor.

To get state tax credits and for the project to advance, the building would need to offer affordable housing, Mr. Gallo said. The developers also got some preliminary indication that the state is willing to give them the full $2.5 million Restore NY grant that was awarded to the original hotel project, Mr. Gallo said.

Empire State Development Corp. had reduced that amount to $1.8 million after the developers determined the hotel was not economically feasible, so they changed the scope to housing.

The developers plan to submit the application for state tax credits after they get a design team, contractor and consultants on board.

The developers hope to obtain between $4 million and $5 million in state tax credits, Mr. Gallo said. The investors may end up contributing between 15 percent and 30 percent for the project, he said.

During the presentation, Mr. Gallo said he hopes the city will agree to a 15-year tax abatement deal, while acknowledging the city has given mainly 10-year agreements to previous housing projects.

The Arditos, who attended the meeting, and Mr. Treanor have been involved in the project since its inception. Mr. Gallo, who has experience in renovating landmarks into rental units, joined the efforts last winter after the project had stalled.

In other business, the council and Advantage Watertown members agreed they will improve communication with each other. The meeting was set up after some council members questioned the group’s role in city government.

Advantage Watertown was formed about eight years ago as the result of combining three city committees. The group of business and community leaders meets monthly to brainstorm and discuss city issues.

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