Both Lappartient and Cookson have said they were confident of getting 30 of the 45 delegates' votes in Thursday's election.
Yet McQuaid, who was beaten by Britain's Cookson four years ago after two four-year terms, says European votes will swing the contest although other elements could come into play.
Europe has 15 delegates, Oceania has three while Asia, America and Africa each have nine.
"If they (European delegates) do vote as one I would say Lappartient will win it because he would just need eight extra votes," McQuaid said on Wednesday at the road cycling world championships in Bergen, Norway, which he was attending in a private capacity.
"I know a few he's definitely getting."
Both Cookson and Lappartient did not respond to Reuters' requests for interviews ahead of the election.
McQuaid, however, believes many of the delegates are not knowledgeable enough about the sport.
"Among the 45 delegates coming from five different continents, some of them would hardly tell the difference between their front wheel and their back wheel," the Irishman said.
"Among them, how many really understand the needs of the UCI? Very few understand it. To win you have to convince those guys that you are the best, and it's not a question of programme. That's where Lappartient will score because he is outgoing."
Africa could also play a significant role on Thursday because the head of the African confederation, Egypt's Mohamed Wagih, could influence the continent's nine delegates to vote in a particular way, McQuaid said.
"Their president is decisive, he can influence his nine delegates," he said.
(Reporting by Julien Pretot; Editing by Toby Davis)
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