Allen noted that Apollo 17, the last spacecraft to fly a mission to the Moon, was housed in Houston. He also added that almost all astronauts are trained for their missions there. NASA's mission control is also in Houston.
Two Houston residents who lost their spouses in the 2003 Space Shuttle Columbia accident will also appear at the press event.
Despite losing close relatives in a space shuttle accident, Evelyn Husband-Thompson and Jon Clark of Houston both said one of the other shuttles should go there. NASA is also retiring the Atlantis and Endeavour space shuttles after their final flights this year.
"Houston is nicknamed the Space City," Husband-Thompson said. "The sports teams are the Houston Astros and the Houston Rockets. The whole town is proud of its legacy with the space program."
"Columbia didn't come back in tact, but at least it came back to Houston, which was some comfort," Clark added.
Several museums are vying to house the shuttles. Among them are the Intrepid Sea, Air and Space Museum in Manhattan, the Museum of Flight in Seattle, the Kennedy Space Center in Florida, and the California Science Center in Los Angeles.
Washington's Smithsonian National Air and Space Museum is generally considered to be the frontrunner for the Space Shuttle Discovery, which returned from its final flight this month.
The group said 58,000 letters have been written to President Obama and members of Congress in favor of bringing one of the shuttles to Houston.
The final decision will be made by NASA administrator Charles Bolden, who the Houston groups points out has recently said he has a soft-spot for the Texas city.
"If I were not the NASA administrator, I would say the places that should get an orbiter are Houston, the Cape [Canaveral]," Bolden said in an interview with the TV station KTRK in Houston.
"Any place that played a vital role in the design, development and operation of space shuttle," he concluded.
The day NASA announces where the space shuttles will be retired will be the 30th anniversary of first space shuttle launch, which was on Columbia, and the 50th anniversary of human space flight.