On the condition of anonymity, the league's 10 coaches participated in the poll. Each chose his top two candidates among schools not currently in a Power 5 program.
Houston and BYU each received five votes.
"At the University of Houston we are certainly honored to be mentioned as a progressive institution that places a competitive emphasis on both academics and athletics," Houston Vice President for Athletics Hunter Yurachek said in a statement. "As a Tier One research institution and Phi Beta Kappa member, Houston has seen a reinvigorated spirit in Athletics. We have returned our proud University to the national spotlight and we aim to compete on the highest levels as we build Champions for Life. Our mission will not change."
With the exception of independent BYU and the Mountain West's Colorado State, all of the expansion candidates are members of the American Athletic Conference.
To exit the American, members must provide 27 months' notice and pay a $10 million exit fee.
The Mountain West's exit requirement is only to provide one year's notice. If that is not provided, a university must pay the conference $5 million or double the school's final year's conference revenue, whichever amount is greatest.
On Tuesday, the Big 12 authorized commissioner Bob Bowlsby to begin exploring expansion candidates.
Bowlsby said the league would consider adding two or four teams. He also added the league would consider several factors, including strength of athletic program, fan base, media market, reputation and academic standing. The league would most likely add the new schools by the 2018 academic year.
The Big 12 won't give full shares to new members upon arrival. It's common practice for incoming schools to receive partial revenue shares for a few years. TCU and West Virginia just finished their fourth seasons in the Big 12 and for the first time received full shares. That means for several years, the current 10 members share the new money. And which schools are willing to accept less money for the longest period of time could help determine whether an institution receives an invitation from the Big 12.
The Big 12 coaches were in Bristol, Connecticut, on Wednesday as part of their annual "Car Wash" on ESPN's campus.
Information from The Associated Press was used in this report.