The US Anti-Doping Agency has released 1000 pages of testimony in which it says the winner of seven Tours de France had been involved in the "most sophisticated, professionalised and successful doping programme sport has ever seen".
"The UCI received the dossier two days ago, 1000 pages, and so our lawyers are studying that at the moment and we have 21 days to come up with a response," McQuaid said.
"So we will do that and it will be wrong of me to second guess or preempt what our lawyers might decide, so the UCI will wait until that work has been done and then the UCI will make a statement."
The UCI must decide its response within 21 days of receiving the file and say whether or not it will appeal to the Court of Arbitration for Sport against USADA's decision to strip Armstrong of his Tour de France titles.
"That will be sent in the 21 days...in the legal department, I've told them that is a priority, that we get this job done as quickly as possible, and within that time frame we will be back," he said.