Verstappen bounced back from an error-strewn first six races of the season, which included clashes with both Hamilton and Vettel, to secure a career-best fourth in the championship.
The 21-year-old outscored everyone except 2018 champion Hamilton across the nine races after the summer break, to end the year with two wins and 11 podiums in total.
Hamilton and Vettel both vouched for Verstappen when asked by Motorsport.com if the youngster was ready to push for a world championship.
“Max has been driving very well throughout the year and has shown his consistency and has been up here many, many times with us,” said five-time world champion Hamilton.
“So, if his team does the job and delivers a platform with which he can compete even closer with us, then of course he’ll be in the fight.”
Red Bull made strong progress with its RB14 this season but Verstappen’s hopes will likely depend more on his team’s new engine partner Honda.
Verstappen’s five F1 victories have been scored with Renault power but the French manufacturer appears to have been at least equalled by its Japanese rival.
Vettel, who won all four of his titles with Red Bull, said: “On the track, I don’t think he needs any advice. I think he’s got all the ingredients.
“There’s a couple of guys out there who have these qualities and Max is certainly one of them.
“I also remember from my time, it’s important to have a competitive package throughout the season and Red Bull are certainly very, very strong.
“I think they put more performance to their car than any other team across the year, so obviously that allowed them to be very competitive.
“Max and Daniel [Ricciardo, Verstappen’s teammate] have proven that they can be very, very quick and very consistent so I’m sure [we will see] more of him.”
Verstappen overhauled Mercedes driver Valtteri Bottas to steal fourth in the championship and was only two points from beating Ferrari’s Kimi Raikkonen.
He would have been third but for several high-profile incidents through the season, including crashing with Ricciardo in Azerbaijan and controversially losing victory in the penultimate race in Brazil after contact while lapping Esteban Ocon.
“I always find that a really difficult question, because you’re so dependent on the package in Formula 1,” said Verstappen in response to his rivals’ answers.
“When I was watching back in the day, it seemed like Lewis was ready for the title in his first year .
“You can always do things better but I think that’s every year. Even if you win the title, there are always things which you can do better.
“So, even if we have a winning package, there will be weekends where you make a mistake, or it can be a better weekend overall. Hopefully first we’ll have that package.”
Max Verstappen, Red Bull Racing RB14
Photo by: Joe Portlock / LAT Images