Lance Armstrong made the personal apology during private conversations in Austin, Texas, a foundation spokeswoman said.
His interview with Oprah Winfrey is due to be aired on Thursday, January 17.
Lance Armstrong, 41, was stripped of his seven Tour de France titles by the sport’s governing body last year. He has maintained his innocence.
“He had a private conversation with the staff, who have done the important work of the foundation for many years,” Livestrong Foundation spokeswoman Katherine McLane was quoted as saying by Reuters.
“It was a very sincere and heartfelt expression of regret over any stress that they’ve suffered over the course of the last few years as a result of the media attention,” she added.
Lance Armstrong, who also received a lifetime ban from governing body the International Cycling Union (UCI) and the US Anti-Doping Agency (USADA), was reportedly close to tears.
It was not quite a confession of sustained cheating, but that is what many in the cycling world and across America are expecting to hear when they tune in to the cyclist’s interview on January 17.
The recording of the TV interview – his first since being stripped of his wins – started later on Monday.
A spokeswoman for the Oprah show said last week that Lance Armstrong was not being paid to appear and that Oprah Winfrey was free to ask him any question she wanted.
The choice of America’s favorite agony aunt to conduct the interview suggests that Lance Armstrong is prepared to make some kind of confession.
At the weekend, Lance Armstrong told the Associated Press: “I’m calm, I’m at ease and ready to speak candidly.”
He declined to go into further details.
Lance Armstrong ended his fight against doping charges in August 2012.
In October, USADA released a 1,000-page report saying he had been at the heart of “the most sophisticated, professionalized and successful doping programme” ever seen in sport.
Lance Armstrong also later resigned as chairman of the Livestrong Foundation, the cancer charity he created.
His lawyer, Tim Herman, has described the USADA report as a “one-sided hatchet job” and the cyclist himself has accused the agency of offering “corrupt inducements” to other riders to speak out against him.
It is believed he is considering an admission because he wants to resume his athletic career, and has shown an interest in competing in triathlons.
Lance Armstrong has reportedly held recent discussions with other cyclists who have themselves confessed to doping.
But there are a number of obstacles to a full confession.
The New York Times has reported Lance Armstrong’s supporters are concerned he could face perjury charges if he confesses to using performance-enhancing drugs, because he made sworn testimony in a 2005 court case that he had never done so.
In addition, Lance Armstrong faces a number of legal cases.
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