The Russian government has told the IOC it will not discriminate against gays during the Olympics, but has defended the law.
White said after Wednesday night's card in Indianapolis that he wants to hold a UFC show in Russia.
"We've got to go there first," he said of co-owner Lorenzo Fertitta. "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 law and the uproar surrounding it, White said: "No, I know nothing about it."
White 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" when it comes to "ethnic background, heritage, color, race, national origin, age, religion, disability, gender or sexual orientation."