Verstappen is widely-regarded as one of the sport’s brightest prospects and Red Bull have tied him down for the long-term as a result.
The Milton Keynes-based team have failed to deliver a car capable of truly contending with Mercedes and Ferrari though.
And they could be in for a season of transition next year as they take on Honda engines after ditching Renault.
Max Verstappen will be hoping he can challenge the likes of Hamilton and Sebastian Vettel regardless of the change.
But he says the onus is on Red Bull to give him the right car to replicate the feats of the multiple F1 title-winning duo.
“Lewis has been fighting for titles since his first season,” Verstappen said, ahead of the Brazilian Grand Prix.
“Are you ready for it? You’re not sure. Was he? Maybe yes, maybe not.
“It’s never 100 per cent clear if one is ready or not but as soon as you have that car, you’re just going to drive it as fast as you can and if it’s the fastest car on the grid, you’re normally winning races or you are second.”
Former F1 driver Jolyon Palmer has outlined what Verstappen needs to do in order to compete with Hamilton.
“In terms of outright speed, he might be the closest to Hamilton,” Palmer said.
“His pace is ferocious, and if he can manage to consistently temper the aggression he showed earlier in the season, which too often got him in to trouble, then he could be a serious threat to Hamilton.
“Verstappen showed how dangerous he can be in Mexico, dominating the entire weekend, albeit pipped to pole by team-mate Daniel Ricciardo.
“It was about the only lap Ricciardo was quicker than Verstappen all weekend.
“Verstappen’s race was also exemplary, defending well against Hamilton at the first corner before showing very strong pace, tyre management and race management to cruise home to a comfortable win.
“The Red Bull car is his only obstacle to a championship bid for next year, particularly its engine.
“But with a switch from Renault to Honda next year, there is much optimism within the team.
“Honda have made great progress over the past few years and seem now to have a better engine than Renault.”
Verstappen goes into Sunday’s Brazilian Grand Prix off the back of a win in Mexico City last time out.