The UCI have admitted they accepted a donation of more than $100,000 from Armstrong in 2002, but have strongly denied it was connected to any cover-up of a positive test.
Tyler Hamilton, Armstrong's former US Postal team-mate, has testified that Armstrong bragged that he had managed to have a positive finding covered up.
Around the same time, the head of a drug-testing laboratory in Lausanne admitted to having met Armstrong and, separately, being given free use of a blood-analysing machine by the UCI.
A report by the United States Anti-Doping Agency last week labelled Armstrong a "serial cheat" and a bully who enforced "the most sophisticated, professionalised and successful doping programme that sport has ever seen".
Dr Michael Ashenden, acknowl-edged as the foremost expert in blood doping and the man whose test caught Hamilton, said there were clear conflicts of interest.
Ashenden told the BBC Radio 5 Live programme, Peddlers – Cycling's Dirty Truth: "The UCI should never have accepted money from Armstrong under any circumstances. But if they took money after they were aware there were grounds to suspect Armstrong had used EPO, it takes on a really sinister complexion.
"We know Armstrong paid the UCI more than $100,000 and, around that time, the UCI gave the Lausanne laboratory free use of a blood analyser worth $60- $70,000.
"That's what I mean by a triangle: the laboratory meets with Armstrong, all of this takes place at about the time that Floyd Landis and Tyler Hamilton said under oath that Armstrong bragged he had managed to have a result covered up."
Dick Pound, the former president of the World Anti-Doping Association, said the UCI could have made greater efforts to catch drug-taking cyclists.
"They could certainly have done things to ensure they caught more people," he said. "It's generally acknowledged now that, for a governing body to promote its sport and to police it, puts them in an impossible conflict.
"The UCI have always been in a difficult position and their behaviour has not always been what you would hope it to be.
"There was certainly generalised knowledge that there had been some payments from Armstrong to the UCI. It's hard to think of the UCI as a charity and Lance somebody filled with [charitable] spirit."
A former aide of Armstrong's told the BBC programme that she was used as a "drug-runner" during her time working for the US Postal team.
Emma O'Reilly, who was Armstrong's personal masseuse and assistant in the 1990s, says she rented a car to travel to Spain to pick up tablets from Johan Bruyneel, the US Postal team director, before returning to France and giving them to Armstrong.
"I went down in an unmarked car, a good six hours' drive, and also that was another reason I knew it was something [untoward] because Lance had said to me, 'don't tell your boyfriend'," she said.
"There's no way in hell am I going to bring him down, crossing over a border [and] pick up a package. Basically, as I used to say to some of the soigneurs [team assistants], 'you are drug-runners', and that's what I was being for the weekend. And to involve [her boyfriend] in it, without letting him know that 'here, you can come with me if you want, but here's what I'm doing'. . .
"So we went down, six hours down that way, Johan gave me the tablets, very discreetly, without letting anybody else know that I was getting them, and the following day we went back to France and then, the following morning, I met Lance in the car park at McDonald's and just handed them over."
On Friday, Bruyneel quit as general manager of the RadioShack Nissan Trek team by mutual agreement, having chosen to contest the USADA charges in an arbitration hearing.
The USADA report states one rider testified "his use of prohibited substances was performed at the direction and with the full knowl-edge and approval of team director Johan Bruyneel".
The UCI were not available to comment but have previously vehemently denied there was a cover-up of any positive test by Armstrong.
Team Sky, meanwhile, have stated that they carried out checks on the Dutch doctor they employed who was working for Rabobank when two of that team's riders were suspended for drugs use.
Geert Leinders was a doctor for Rabobank when Michael Rasmussen was kicked out of the 2007 Tour de France and when Thomas Dekker tested positive for EPO.
A Team Sky spokesman said: "Dr Leinders worked with Team Sky on a freelance basis and his contract has now ended."