LYNN – The City Council will hold a public hearing Tuesday on a proposal by the All-Care Visiting Nurse Association (VNA) to construct a new headquarters on Broad Street.The VNA plan calls for a four-story building adjacent to the Massachusetts Bay Transportation Authority train and bus terminal on Market Street.Shawn Potter, executive director of the Lynn VNA, said the organization has outgrown its present quarters in City Hall Square.Although the project plans apparently have undergone some changes as a result of negotiations with city officials, the VNA’s status as a non-profit organization remains the same. From its inception, critics of the VNA plan have said the city would be better served by a for-profit developer interested in building on the site, since non-profits do not pay real estate taxes.In the latest turn of events, Mayor Judith Flanagan Kennedy on Friday acknowledged that an annual payment in lieu of taxes has been discussed with the VNA and with other non-profit organizations in the city.City Council President Timothy Phelan confirmed as much.According to Phelan, the VNA has worked out an arrangement with the city to make an annual payment that would help offset the loss of property tax revenue.”The VNA has worked out the concerns expressed by a lot of city officials, residents and our development team,” he said, explaining that the issues involved density, overcrowding, congruity with existing urban improvement plans, exterior lighting and neighborhood parking.The revised plan reduces the building footprint from 17,500 to 11,500 square feet, and the number of stories from five to four. “The reduction in footprint was done solely for the purpose of maintaining green space,” Phelan said.The VNA has also committed to creating a park with a walkway, benches and landscaping on the Market Street end of the building, he said. Shrubs and mature evergreen trees are part of the agreement and will help make the building more akin to North Shore Community College and its landscaping across the street.”This project is going to improve that area 100 fold,” Phelan said. “We fully support the idea of an office building with people working downtown who will buy newspapers or snacks and eat lunch in the local restaurants. The land is zoned for light industrial, which means anything that falls within that description could go there.”The VNA will have some surface parking, but only for handicapped drivers. Employees will park in the adjacent MBTA parking garage once the VNA completes an agreement to lease a specified number of spaces, Phelan said.”The VNA will basically be renting spaces in the garage from the T,” he said. “Another good thing is that this brand new office building will block out the ugly aesthetics of the garage and for the first time give the garage a substantial use. So it’s really a win-win.”Phelan praised the VNA for committing to the annual payment. “To their credit, they did it because they want to work with the city. The VNA has a long history with the city and they want to be good neighbors.”If the proposal receives council approval Tuesday, the VNA hopes to complete the construction within 14 months.The public hearing is part of the council meeting, which begins at 8 p.m.