The Briton won his fourth drivers' world championship at the Mexico Grand Prix this year and following the final race in Abu Dhabi, he was hopeful that more drivers will enter the battle for the title next season.
Hamilton named himself, Fernando Alonso, 2017 title rival Sebastian Vettel and Max Verstappen as the four strongest drivers in the sport at the moment, and Horner believes that the former McLaren driver would be "foolish to underestimate" Daniel Ricciardo, who has proven to be one of the top drivers in recent years.
"The four strongest drivers I think are me, Fernando, Sebastian, Max. I really hope we are all in the fight next year," Hamilton told Motor Sport Magazine.
The Australian driver, who partners Verstappen at Red Bull, has consistently challenged for a podium position in recent seasons whenever his team were able to provide him with a car to challenge the dominant Mercedes team.
The Austrian energy drink owned team, alongside Ferrari, have been the main challengers to the Silver Arrows in the last four years and are likely to do so again in 2018. Despite the Italian team and Mercedes battling for the title in 2017, Ricciardo managed one race win and eight podiums, and it would have been more had he not been plagued my reliability issues — the Australian suffered six retirements.
"Lewis would be very foolish to underestimate Daniel," Horner told Sky Sports. "He's a phenomenal driver, he's arguably the best overtaker in the business. He's driven some great races this year and some great races in his time at Red Bull.
"He's absolutely ready for a championship challenge if we can provide him with the tools to do the job," the Red Bull Racing chief added.