Mercedes has won every constructors' and drivers' championships on offer since 2014, with Hamilton missing out on the top prize just once in 2016.
After a strong end to the 2019 season, Red Bull is being tipped as title contenders in 2020, with Verstappen set to lead the charge for the energy drink-backed squad.
Ferrari has stated that it does not expect to be the fastest car at the season-opening race in Austria in under two weeks' time, as it enters the year off the back of a difficult 2019 campaign.
Speaking to Ziggo Sport, Webber doesn't see the Scuderia outfit as challengers this year, predicting that the title fight will run between Verstappen and Hamilton.
"It will go between Max Verstappen and Lewis Hamilton,” Webber said. “I don't see anyone else who can participate in the fight for the world title. Ferrari will not be there this year. At the moment there's no one else that can handle Lewis but Max.”
2020 will be Honda's second year in partnership with Red Bull, with the Japanese manufacturer securing three wins with the team last year.
While Webber expresses full confidence in Red Bull and its potential, he affirms that Honda must step up to consistently challenge Mercedes during 2020.
"I have confidence in Red Bull, in their aerodynamics department and how they work as a team,” he said. “The only question is whether Honda can arm itself against Mercedes all season.
“Mercedes probably has a little more power, and then you can also drive with more downforce and make your life a little easier.”
The 2020 season will get underway from July 3 - 5 at the Red Bull Ring in Austria, where Verstappen has won two years in a row.
Bahrain International Circuit - Winter testing