"We are not going to talk about whoever is involved or whoever is in my life. If somebody takes a picture they can put two and two together," the seven-time Tour de France champion told The Associated Press.
Armstrong and Crow split last February. The couple met in October 2003 and began dating shortly after. They announced their engagement in September 2005.
"It's so hard," the 35-year-old Armstrong said Monday. "It puts too much strain and unrealistic expectations on a relationship when you put it out there. It's tough when you love somebody and you want to be with them, you want to talk about them. It's not easy, but I think it is by and large better not to talk about it."
Armstrong also told the AP that he plans to return to the New York City Marathon this year. He ran the marathon for the first time in November.
"I'm gonna do it again," Armstrong said during a break from a meeting of the President's Cancer Panel. In 1996 Armstrong was diagnosed with testicular cancer that spread to his abdomen, lungs and brain.
The panel visits four cities a year, holding daylong meetings to gather information about cancer treatment and prevention. On Monday, the panel's meeting focused on research and public policy about tobacco.
"Smoking is something that is clearly deadly, not just for the people that choose to do it but for the people around them as well," said Armstrong, who has been a member of the panel since 2002.
Armstrong, who has retired from cycling, said the size of the New York City Marathon will help fundraising possibilities for his charity, The Lance Armstrong Foundation.