Councilors Colin LePage, Mary Ellen Daly O'Brien said John Michitson said they will also vote yes.
"Times they are a changing," Michitson said, quoting Bob Dylan.
The local-option law was originally proposed by Dave Andelman, creator of the “Phantom Gourmet,” a popular television show that critiques restaurants. Andelman formed the Restaurant and Business Alliance in 2010 to push the extended Sunday hours and other legislation to help restaurants.
Vincent Errichetti, executive director of the restaurant lobby, said Haverhill's adoption of the law will help restaurants here compete with restaurants in nearby New Hampshire.
"As (Haverhill) is a border community, it is nice to give New Hampshire (residents) a reason to come to Haverhill," Errichetti said.
Edwards said the commission is taking up the measure now at the request of The Barking Dog Ale House, a new downtown restaurant that opened several months ago on Washington Street.
Representatives from two other Haverhill restaurants have also indicated their interest in the extended Sunday hours. Ivan Yee, who owns Oriental Gradens, and Sharon Cohen, who manages The Tap Brewhouse, both said they support passage of the local-option law.
On days of the week other than Sunday, Haverhill restaurants with liquor licenses can serve alcohol from 8 a.m. to 1 a.m., or until 2 a.m. on Saturdays.