By Holly Yan, CNN

(CNN) -- His planned speech at Texas A&M University has been axed, but another university could still host white nationalist leader Richard Spencer.

Spencer, who helped found the so-called alt-right movement, is the president of the National Policy Institute. And that group has asked to rent space at the University of Florida for an event featuring Spencer on September 12.

University of Florida President W. Kent Fuchs said the event is still under discussion and has not been finalized.

"This organization is unaffiliated with the university, and no student groups or other groups affiliated with the university are sponsoring this speech," Fuchs said in a letter to the Gainesville campus.

But according to the university's policy, "non-university groups, organizations and persons may rent space on campus, provided they cover rental expenses and security costs like all other third-party renters," Fuchs said.

That's not to say he wants Spencer on campus. He doesn't.

"For many in our community, including myself, this speaker's presence would be deeply disturbing. What we've watched happen in Charlottesville ... is deplorable," Fuchs said.

"While this speaker's views do not align with our values as an institution, we must follow the law, upholding the First Amendment not to discriminate based on content and provide access to a public space."

Heightened fears after Charlottesville

Two days after a driver mowed down a crowd denouncing white supremacists in Virginia, Texas A&M University nixed a planned white nationalist protest, citing safety concerns.

White nationalists, neo-Nazis and other extremist groups had planned to hold a "white lives matter" rally at Texas A&M on September 11.

The canceled event, which Spencer was supposed to headline, was inspired by the "Unite the Right" rally in Charlottesville, according to Texas A&M's student newspaper The Battalion.

Spencer had already spoken at Texas A&M in December, speaking about white supremacy for two hours to a room of 400 people -- the vast majority being protesters.

"At the end of the day, America belongs to white men," he said at the time.

Controversy over Spencer's December appearance led the school to later change its campus speaker policy. Now, outside groups or individuals to have sponsorship from a university-sanctioned group to reserve campus facilities.

And Preston Wiginton, the man who was organizing the "white lives matter" rally, didn't have that campus support.

"None of the 1,200-plus campus organizations invited Preston Wiginton nor did they agree to sponsor his events in December 2016 or on September 11 of this year," Texas A&M said in a statement.

"Linking the tragedy of Charlottesville with the Texas A&M event creates a major security risk on our campus."