Boston City Councilors John Tobin (Jamaica Plain, Mission Hill) and Paul Scapicchio (East Boston, North End) want to move – offices, that is.

The two councilors have teamed up to suggest a plan to move City Hall from its current location in Government Center to the Hynes Convention Center, Tobin said in a telephone interview Tuesday.

The proposal, which will be considered at a hearing sometime in March, stems from what Tobin called the “environmental inefficiency” and “just plain ugliness” of the current City Hall.

Built in the “Brutalist Modern Style” between 1965 and 1968, the building “doesn’t match the characteristics of the surrounding buildings” in the 11-acre Government Center Plaza, Tobin said.

The plaza itself is also “a dead area,” said Joe Arangio, a Scapicchio aide. The acreage is largely under-used, he said, with only an occasional concert or sporting event. Over a number of years, six task forces have looked at possible changes to the plaza’s layout to make better use of the valuable land.

The plaza is worth an estimated $25 million an acre, Arangio said. The “collateral benefits of such a sale are substantial,” he said, adding that the city is “strapped for cash.”

“Where else is there virgin land in a major city in the country?” he said.

The City Hall building itself is 11,000 square feet – which means big energy bills, Tobin said. To address the environmental issue, an audit of the building’s energy use will be presented at the March hearing.

Historically, City Hall has occupied five other Boston buildings, including Faneuil Hall, the Old State House and the Old County Court House.

The councilors’ proposal also provides a plan for Hynes Convention Center, which may lose business when the new Boston Convention and Exhibition Center on the South Boston waterfront opens in June of this year.

“If word comes down that Hynes won’t make it, we have to have a plan,” he said. Buying the Hynes Center would be “killing two birds with one stone.”

But some have objected to the idea of moving City Hall to Hynes, Arangio said. The Department of Travel and Tourism considers Hynes essential to a number of small businesses in the Back Bay area where the convention center is located, he said. Additionally, small conventions may still want to use the Hynes, even after the bigger, newer convention center opens.

Councilor Michael Ross (Fenway, Back Bay) also said a move to the Hynes would do more harm than good.

“Local businesses depend on the [Hynes] Convention Center to keep them going,” Ross said in a telephone interview Wednesday. Using the building as a new City Hall “would hurt the city and reduce the tax revenues we depend on in order to operate,” he said.

Ross also said selling the current City Hall building may not make economic sense.

“While it’s ugly to some, that’s a subjective opinion… The idea’s been surfacing for years, but we don’t make decisions based upon subjective opinions,” he said.

Though Tobin has been in Iowa attending the Democratic caucus, he said that the general public response to the proposal in emails and phone calls has been positive.

And what would become of the City Hall building if it were sold?

“Probably torn down,” Tobin said, “It still remains a big brick desert.”