The City Council next week could vote on whether the dilapidated Savin Hill home at 24 Grampian Way should be designated a local landmark.

The council’s economic development committee, chaired by Councillor Bill Linehan, held a hearing on the landmark status on Thursday. The Landmarks Commission voted 9-0 on Nov. 26 to designate the home as a landmark, and Mayor Thomas Menino signed off on the designation the following day.

The home is largely associated with George Wright, an American sports figure whose family bought the home in 1887. Ellen Lipsey, the executive director of the Landmarks Commission, said in her testimony to the council that the “fanciful, Stick Style of the house (and the stable, which was taken down for safety reasons prior to designation) was built by William Prescott Hunt, a wealthy industrialist. John Kehew, a maker of nautical instruments and an oil merchant, purchased the property from Hunt and Kehew was the first occupant of the house.”

Lipsey added that in the last 20 years, there have been 27 landmark designations and the council has approved all of them. Lipsey’s comment prompted Linehan to respond, “But this is a process and we get the opportunity to weigh in.”

The 13-member council can override the mayor with a two-thirds vote. Six councillors are on record opposing the landmarks designation: City Councillors At-Large Stephen Murphy and Ayanna Pressley, District 9 Councillor Mark Ciommo, District 6 Councillor Matt O’Malley and Linehan. District 3 Councillor Frank Baker, who lives diagonally across from the home, had also weighed in against the designation, but recused himself after questions were raised by local civic activists who said that he may have a conflict of interest due to living near the house and his brother making an unsuccessful attempt to buy it.

Linehan and O’Malley were the only two councillors who attended the hearing, which lasted about an hour. Asked afterwards if there are enough votes for an override, Linehan said, “I don’t know. I didn’t count them.”

“I think we will have to see what happens on Wednesday,” Linehan added.

Linehan said he had concerns about the preservation of a particular property becoming a restriction on the property owner’s ability to redevelop or fix up a home. The family of the late Ray Tomasini, which owns the property but did not testify at the council hearing, has argued for the demolition of the home, saying landmark status would impact their ability to redevelop the property.

Linehan added that the Tomasini family has lived inside the house for longer than some of the home’s more famous tenants. “And so that’s a different story to me,” he said.

Linehan offered a hypothetical example: If he and his family owned a home but the city desired to designate it a landmark because a celebrity like Red Sox slugger Ted Williams had lived there, “that doesn’t seem to right to me,” he said.

During the hearing, Linehan said he hadn’t yet made any decisions on where the matter goes from there. But, he added, “I hear the place is a real dump.”