Hamilton, who arrived south of the American border on Wednesday, needs to finish only seventh to be sure of his fifth title.
But the Briton, 70 points clear of Ferrari’s Sebastian Vettel with only 75 remaining, will want to make up for his failure to win last weekend by taking the chequered flag on Sunday.
Verstappen, 21, was victorious in Mexico last year, and the Red Bull driver, fresh from his impressive run from 18th to second in Austin, Texas, believes he has the car underneath him to triumph again.
“This is definitely the best chance for me to win out of the last three races,” he said.
“In qualifying, we may not have a chance, but in the race we seem to be working well, so I expect this to better than Austin.
“But Lewis will want to win, so I don’t think that will change anything.”
The high altitude of the Autodromo Hermanos Rodriguez, which sits 2,200 metres above sea level, acts as an equaliser in engine performance.
Therefore, the Renault in the back of Verstappen’s Red Bull, usually inferior to the might of Mercedes and Ferrari, is likely to be closer this weekend.
“Performance at altitude is more about mechanical grip, and our car is very good mechanically,” Verstappen added.
“That is why we will be more competitive on this track than others, even if there is a super-long straight. Physically, the high altitude is not a big deal.”
Hamilton clinched his fourth championship in Mexico last year, despite crossing the line only ninth after colliding with Vettel on the opening lap.
Vettel, who made the eighth and ninth errors of his mistake-ridden campaign in the US last weekend, must also win on Sunday to stand any chance of stopping Hamilton.
But the German driver arrives here under a cloud following his recent troubles.
For much of this season, Ferrari have had the superior machinery over Mercedes, but it is Hamilton who is set to prevail with, for the second season running, two rounds to spare.
Would Verstappen have won the title for the Scuderia?
“I am not driving for them, so I don’t want to comment,” came his diplomatic response.
Asked why he felt Vettel had made so many mistakes this season, he replied: “I can only look at myself so it makes no sense to speak about another driver. I don’t want to p*** anybody off.”
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