Gov. Greg Abbott has called for tweaking the state's highly controversial Top 10 Percent Rule for college admissions, another sign that the law could be at risk when the Texas Legislature convenes in 2017.

In an interview with the University of Texas at Austin alumni magazine The Alcalde, Abbott said UT-Austin should be given more latitude in whom it chooses to admit. The rule, which has been law since 1997, promises automatic admission into any Texas public university to students who finish in the top 10 percent of their high schools' graduating classes. Currently, the overwhelming majority of Texans admitted into UT-Austin get in because of the policy.

The rule was designed to promote diversity at the state's top universities. Texas public schools are largely segregated, so promising admission to the same amount of students from minority-dominated schools and white schools — regardless of standardized test scores — in theory helps minorities.

But in the interview, Abbott expressed doubt about whether it is making much of a difference.

"If you look back to the university that they had before the automatic admissions compared to what they have now," Abbott said, "it’s my understanding it was fairly much the same."

When the law was passed in 1997, black and Hispanic students made up 16.1 percent of the student body. At the start of this school year, they made up 23.4 percent, though it's difficult to say how much of that growth is due to state demographic changes unrelated to the law.

Read MoreThe history of the Top 10 Percent Rule

What is clear is that the law has been deeply unpopular among some lawmakers, educators and parents. Many suburbanites despise it; they say the law is unfair to people from their schools, where it is harder to crack the top 10 percent. Meanwhile, UT leaders have expressed frustration about how it takes away their ability to build their student body to their liking.

Late last decade, so many students from the top 10 percent were applying to UT-Austin that the school seemed poised to run out of room for anyone else. In 2009, the rule was amended so that UT-Austin could cap its automatically admitted students to 75 percent of in-state students who enroll. Some UT-Austin supporters believe that even that is too high. UT System Chancellor Bill McRaven has been critical of the law, saying that it might be hurting UT-Austin in national rankings.

Abbott, apparently, agrees with those concerns.

"The University of Texas needs to have greater latitude," he said, according to the magazine.

Asked whether he meant that the cap should be lowered or "maybe lowering the percentage of the class that gets automatically admitted," Abbott replied: "Exactly."

Lawmakers consistently raise the idea of eliminating or changing the Top 10 Percent Rule, but so far minority and rural lawmakers have banded together to stop it. There are signs, however, that 2017 could be different. The law has played a key role in Fisher v. the University of Texas at Austin, a lawsuit about the constitutionality of affirmative action. Some lawmakers may have been hesitant to change the law while that case was still pending. But the U.S. Supreme Court is expected to rule on the issue in the next month — well before lawmakers meet again in early 2017.

Meanwhile, State Rep. John Zerwas, R-Richmond, chairman of the House Higher Education Committee, has expressed support for the idea of lowering UT-Austin's cap. Other legislators have agreed.

The Top 10 Percent Rule was one of several controversial issues that Abbott weighed in on during the interview with the alumni magazine. The governor, who is a UT-Austin graduate, was also asked about whether he thought the Longhorns should play their old rival, Texas A&M, in football again.

Abbott's answer was one word: "Yes."

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