The driver market has already proved to be pretty quiet this year, with few teams making changes to their line-up. That was put down to the top drivers like Lewis Hamilton and Max Verstappen already being locked into contracts for next season.
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Many drivers are also biding their time to see what happens when Formula 1's new rules and regulations come into effect, which could transform the fortunes and standings of the teams and give impetus to drivers to seek new seats.
But Horner doesn't expect that to be the case, and believes that most of the high profile drivers will opt to remain precisely where they are even in the longer term.
“I think all the top guys are out of contract for the end of next year,” Horner told Motorsport.com.
"[But] if they're sitting in competitive cars next year, why would they swap? Why would they move?
"Ultimately when the music stops I wouldn’t be at all surprised for everybody to end up remaining in the same seats.
Leclerc's under contract at Ferrari. Lewis obviously is pretty happy in his environment. Max is happy in his environment.
In particular, Horner didn't believe that Verstappen would leave Red Bull, despite recent media reports that the Dutch star had expressed an interest to moving to Mercedes when his current contract expires.
"He is very happy in this team," Horner insisted. "We love having him in the team. He fits very well here."
But Horner admitted that Verstappen would only stay put if he believed that Red Bull could give him a chance of competing for the world championship.
"It's down to us to give him a competitive car next year," Horner agreed.
Lewis Hamilton was recently reported to have he's had initial informal talks with Ferrari about a possible move to Maranello when his current contract at Mercedes ends.
Charles Leclerc said he would welcome the prospect of having Hamilton as a team mate, while Ferrari boss Mattia Binotto cryptically said that the idea of Hamilton being a free agent in 2021 "makes us happy".
There's also been gossip that four-time world champion Sebastian Vettel might decide to call it a day, although paddock speculation that he would retire at the end of the current season has proven entirely unfounded.
As a result, Mercedes and Ferrari will start next season with a completely unchanged driver line-up, as will McLaren, Alfa Romeo, Racing Point and Haas.
Red Bull will continue to pair Verstappen with Alexander Albon, who was promoted to the second seat over the summer in place of Pierre Gasly.
And the only change at Toro Rosso will be the team's name as the squad becomes Alpha Tauri over the winter where Gasly will once again be alongside Daniil Kvyat.
But Nico Hulkenberg had departed Renault in favour of Esteban Ocon, while Nicholas Latifi arrives at Williams in place of Robert Kubica. They're the only two race seats known be be changing hands before Melbourne in March.