State Reps. Garnet Coleman and Bill Callegari, both from the Houston area, co-wrote a letter Thursday asking Big 12 officials to consider adding the university to the conference.
"UH is the third largest university in Texas, and is on track to rank among the top research universities in this state," the letter says. "Despite UH's local and statewide prominence, the university does not belong to a strong BCS conference such as the Big 12. The Cougars, the city of Houston, and the state of Texas deserve better."
Houston is a member of Conference USA and was a member of the Southwest Conference until 1995.
Conference USA officials did not immediately respond Thursday to messages left by The Associated Press. Big 12 officials said commissioner Dan Beebe was not available to comment.
The Big 12 is set to lose two schools after Nebraska committed to the Big Ten and Colorado to the Pac-10. Big 12 commissioner Dan Beebe has said the league has no plans to add any teams from within its five-state area, which includes Texas.
Coleman said he is not deterred by Beebe's stance.
"I don't quit," Coleman told the Houston Chronicle. "I don't start something I'm not going to finish. If I didn't think this was a worthy endeavor, I wouldn't have started it. This is the beginning of this effort, not the end."