Facing the possible end of state funding, the nonprofit group that manages the Rose Fitzgerald Kennedy Greenway is seeking more contributions from private sources as well as soliciting the public’s suggested improvements to the 15-acre park system.

Directors of the Greenway outlined plans Tuesday to eventually increase its annual budget to $6 million, a 36 percent increase from its current $4.4 million. But how they will fund that increase remains a work in progress, with directors hoping much of it will come from a voluntary tax on commercial landowners along the downtown parks.

The officials have begun pursuing the creation of a business improvement district, similar to one now in place in Downtown Crossing, where property owners around the Greenway would willingly pay an additional tax for the upkeep of the parks.

And Greenway directors are also trying to reinvigorate a broader discussion with the public and private businesses about the parks: Should there be more festivals and outdoor concerts? What kind of public art should be installed? And could the park system raise money for maintenance by creating amenities such as an ice rink, and renting out skates?

“All of this is up for discussion,’’ said Georgia Murray, chairwoman of the Rose Fitzgerald Kennedy Greenway Conservancy’s board. “We know how much it will cost to run the Greenway. The creative part is where those funds come from.’’

The pressure to raise more money intensified in January when the Massachusetts Department of Transportation warned the Greenway conservancy that the state may eliminate public funding by 2017, at the end of its lease with the state. The parties are negotiating a renewal. The state government is currently responsible for paying half of the conservancy’s budget through 2012 - about $2.1 million this year.