BOSTON — Yellowing grass and flower beds in new Big Dig parks prompted members of a quasi-public board to weigh in yesterday on whether to allow dogs in the downtown greenway.

Members of the Rose Fitzgerald Kennedy Greenway Conservancy board discussed banning dogs from portions of the park, enforcing leash laws and opening a dog park on a designated strip to protect newly planted trees and grass worth millions of dollars.

The plants, sod, trees, and flowers growing on the greenway are fragile and not mature enough to withstand doggie damage, said Nancy Brennan, conservancy executive director.

“It is going to be one of the bigger problems,” said Steven Anderson, the conservancy’s director of park operations.

Peter Meade, the board chairman, said the conservancy should plan to have dog policies in place by spring.

Meade said the conservancy wants to keep canines from doing their business on the city’s green plots and plans to appeal for support from neighborhood residents “who may know the names of their neighbor’s dogs better than they know the names of their neighbors.”

Board members discussed putting up signs and reaching out to community groups about curbing or keeping dogs off park grounds. Meade suggested opening up a dog park on the Greenway’s Parcel 12, which sits between two ramps between Cross and Clinton streets.

Boston Redevelopment Authority manager Peter Gori said city officials are against using Parcel 12 as a dog park because the site is difficult for pedestrians to access and might be used for construction equipment while a nearby park plot is under construction. Gori said the challenge is finding a site close to people living and working in the North End and Chinatown or the Wharf districts, he said.

Other Boston public parks restrict dogs, including the Public Garden where dogs are required to be on a leash. In the Boston Common, dogs are required to be on a leash except in designated areas. The Southwest Corridor Park in the South End and the Charlesgate Park in Back Bay have designated off-leash dog parks.

The city of Boston’s dog fouling law requires dog owners to remove and dispose of any feces left by their dogs on sidewalks, streets and parks. Boston dog owners are also required to keep their dogs on a leash when off home property to protect other residents from free-roaming dogs. According to the Department of Animal Control, there are 7,500 dog licenses issued in Boston.