A private group called the Boston Olympic Exploratory Committee wants to bring the Summer Games to Boston in 2024, and hopes to get Mayor Thomas M. Menino’s blessing to pursue preliminary support from local businesses.

It expects to win the mayor’s approval soon, following a promising meeting with City Hall officials Monday, said committee chairman Eric Reddy of West Boylston.

Two weeks ago, the United States Olympic Committee solicited bids from Boston and 34 other municipalities. The positive report from the Monday meeting at City Hall is the earliest indication the city may give the idea real consideration. Menino has not commented publicly on the USOC’s invitation, and his office did not respond to Globe inquiries.

Reddy said the committee had been working behind the scenes for several months. It has reserved an Internet domain, www.boston-2024.org, set up a Twitter feed, and started a Facebook page — with “likes” from Menino and gold medal-winning gymnast Aly Raisman of Needham, among 342 others.

Boston officials and city business leaders seriously considered a bid to host the 2004 or 2008 Olympics. Eventually, they decided not to submit a proposal, concluding their chances were slim because the United States already had been awarded two Games within six years.

The United States has not hosted the Summer Olympics since 1996, when the games were held in Atlanta, and the International Olympic Committee emphatically rejected recent bids by New York and Chicago. But since accepting a smaller cut of Olympic TV and marketing money under a new revenue sharing agreement with the international committee last May, the US panel is increasingly optimistic the next American attempt could succeed.

Reddy — the senior charitable sales manager at Boston-based Tickets-for-Charity, an online ticket seller that directs portions of sales to nonprofits — and his group appear serious in their Olympic interests.

Even before USOC chief executive Scott A. Blackmun wrote to Menino and other mayors on Feb. 19, Reddy’s group had informed the committee of its interest in organizing a Boston bid for the 2024 games.

The USOC’s response? Get your mayor on board.

Reddy said his group was close after meeting Monday with Christopher Cook, director of the Mayor’s Office of Arts, Tourism & Special Events, and other Menino aides. He hopes to have a letter of endorsement from Menino in hand within a week.

“What we want is a green light to pursue this for, say, five months and see how far we get,” Reddy said. “We would form a [nonprofit organization] and begin to seek donations.”

Reddy, who declined to identify other members of the group, said it planned to meet Tuesday evening with advisers, including Rikk Larsen, who sat on a committee that explored a Boston Olympic bid in the 1990s.

Reddy stressed that his group was “trying to be quiet about this,” and did not want to overhype an effort that remains in its early stages.

Reddy said he and his colleagues have been contacting local business leaders to gauge their interest in backing an Olympic bid. They persuaded Steve Freyer — who chaired the Boston Organizing Committee in the ’90s — to give them his only copy of the group’s old bid prospectus, which outlined plans for venues, lodging, and other logistics.

They also have allies in the state Legislature, including Senator Eileen Donoghue, a Lowell Democrat who in January filed a bill that would create a special commission to study the feasibility of hosting the Summer Olympics.

Staging the games would be a massive enterprise for Boston, likely requiring significant infrastructure improvements. Recent Olympics have cost tens of billions of dollars.

In its letter, the USOC stated that the 2024 host city will need a reliable public transit system, an Olympic village that can accommodate 16,500 athletes, technical support for more than 15,000 media members, and 45,000 hotel rooms to house visitors from around the world.

At present, the cash-strapped MBTA operates with a subway system with some cars that have been in service for 44 years.

There are only about 30,000 hotel rooms in all of Greater Boston, according to the Greater Boston Convention & Visitors Bureau.

In recent cycles, domestic bidding alone has cost prospective hosts more than $10 million.