Russia's law prohibiting promotion of "non-traditional'' sexual relations has provoked harsh international criticism ahead of the Feb. 7-23 Winter Olympics in the Russian resort of Sochi.
The Russian government has told the IOC it will not discriminate against homosexuals during the Sochi Olympics. But it has defended the law, saying it applies equally to everyone and cannot be regarded as discrimination based on sexual orientation.
White said after Wednesday night's card in Indianapolis that he wants to hold a show in Russia.
"We've got to go there first," he said when asked about Russia. "Me and Lorenzo (co-owner Lorenzo Fertitta) are going there. ... We're going to talk to the right people and we're going to figure whether we're going to do this or not."
He said he did not know the date of the visit.
Asked about the controversial Russian law and the uproar surrounding it, White said: "No, I know nothing about it."
White and the UFC have made some missteps in the past on the gay and lesbian front.
The UFC boss apologized in April 2009 for making a gay slur contained in a profanity-laced video blog posted to YouTube in which he lambasted a journalist.
Earlier this year, the UFC suspended heavyweight Matt Mitrione for his verbal attack on transgender fighter Fallon Fox.
It also introduced a code of conduct that prohibits "derogatory or offensive conduct, including without limitation insulting language, symbols, or actions about a person's ethnic background, heritage, colour, race, national origin, age, religion, disability, gender or sexual orientation."