Rippon set off a furore last month by reportedly criticising Pence's views on LGBT rights and then declining when Pence offered to meet. Pence arrived in South Korea on Thursday as head of the U.S. delegation to the Games.
Rippon declined to confirm if Pence had in fact reached out to him, referring queries to the U.S. Olympic Committee.
"I don't want to distract from the competition or make this too much for my competitors and my teammates," he told reporters after a practice session.
"After the competition I'm open to meeting him and having an open conversation, but opening ceremonies are tomorrow and I've been really focused," Rippon, who is taking part in his first Olympics, added.
USA Today cited two unnamed sources in a story on Wednesday that said a member of Pence's staff had tried to set up a conversation between Rippon and the vice president, but the skater declined.
Pence communications director Jarrod Agen told reporters in Tokyo that the report was "false and should be corrected".
"As we’ve said before, the vice president is supporting all the U.S. athletes in the Olympics and is hoping they all win medal," Agen said.
The oldest of six children, Rippon was born with a severe hearing loss that was corrected through surgery when he was nearly a year old. He came out as gay in 2015.
Rippon said he was not having trouble maintaining his concentration.
"If anybody can do it, I can. Because I think I have a lot of experience that my competitors don't - I'm 28, I've dealt with a lot of things in my life and I think at the very core I've always spoken my mind."
Rippon, who has said he could hardly believe he had made it to the Olympics and that seeing the Olympic rings from his room in the athletes' village was incredibly inspiring, said he thought it was important for athletes to speak up - but that he also needed to get through the Games.
"I've been waiting 28 years to be here and I want to do everything I can to stay focussed and ready for this opportunity," he said. "It's my opportunity to show the world what I've got and represent my country the very best that I can."
(Reporting by Elaine Lies; Editing by Amlan Chakraborty and Nick Macfie)
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