Speaking at the Sports Industry Breakfast Club, Cookson said the plan was disrespectful to the Tour, claiming that Armstrong would be advised not to take part.
The Texan had his seven Tour titles taken away in 2012 after he admitted to using performance-enhancing drugs throughout his career and has been banned from taking part in several charity events since.
Cookson said: “I’m sure that Geoff Thomas means well, but frankly I think that’s completely inappropriate and disrespectful to the Tour, disrespectful to the current riders, and disrespectful to the UCI and the anti-doping community,” said Cookson.
“I think Lance would be well-advised not to take part in that.”
Former Crystal Palace captain, Thomas, plans to ride the entire route of the 2015 Tour one day ahead of the peloton and has reportedly persuaded Armstrong to join him for a number of stages.
The reaction to the news within professional was mixed, with MTN-Qhubeka boss Doug Ryder and Team Sky’s Sir Dave Brailsford firmly against the decision, while Tinkoff-Saxo’s Steven de Jongh says he has no issue.