Such a facility could alleviate the current shortages of parking that peak on Thursday, Friday and Saturday nights, as well as whenever a special event is held on or near the Square.
It would take on extra urgency, however, if city officials were to implement proposals to transform much of the existing parking into greenspace - some "forward thinking" that Mayor George "Pat" Patterson assures is years in the future, if it happens at all.
"We're trying to look at all our options," he said.
The committee, which consists of downtown business owners, downtown workers and other residents, will study possible locations, impacts, designs and financing possibilities for a parking garage, among other factors.
Since few towns the size of Oxford have such facilities, members have been encouraged to bring all ideas to the table early on.
"I've asked my committee for now to think without a lot of restrictions," said Ron Hipp, the group's chairman. "Do we need one? If we do, where do we need it? What could it look like? How could it be paid for? Those are the kinds of questions we need to ask." In addition to conventional research, committee members have visited parking garages in smallish towns from Arkansas to Michigan.
Two locations have been tentatively identified for a garage - one fronting on Jefferson Avenue behind the Oxford-University Club, and the other directly behind City Hall.
"If you stand behind City Hall, you're looking at a pretty expansive piece of property. It's got access from Van Buren Avenue, Jackson Avenue and 15th Street," Hipp said. "Plus, you could have the opportunity to exit the garage right onto the Square, and nobody has to walk in an alley."
The lot dips steeply away from City Hall, which could be an advantage in making a three-story structure unobtrusive in the historic district, he added.
Financing would likely be the biggest issue if building a parking garage, and Patterson is adamant that taxes will not be raised to pay for it.
If some form of parking fees were implemented, whether by the city itself or through a public-private partnership, it could serve both to fund the facility and to encourage better use of available spaces.
"A lot of studies indicate paid parking creates more turnover, so more people could visit the Square," Hipp said.
Both Patterson and Hipp say a parking garage is not a certainty.
"It's pretty early in the process," Patterson said. "We're looking at everything."