Currently sixth in the drivers' standings, Perez is over 100 points behind team-mate and reigning champion Max Verstappen.
Despite signing a new contract with the team earlier this year, his poor performances have led to speculation that he may be replaced.
Lawson waiting in the wings
Horner has consistently backed his driver, but patience may be running thin after another miserable weekend at the British Grand Prix, where Perez crashed in qualifying and failed to make gains during the race.
Speaking post-race, the Red Bull chief admitted it had been another 'horrible' weekend for the six-time race winner, but shared some some responsibility for the result.
Horner also confirmed that reserve driver Liam Lawson will test the RB20 this week, as the Kiwi looks to grasp his opportunity to impress.
Lawson already has experience in F1 having replaced Daniel Ricciardo for five races last season, and is eyeing up a permanent seat on the grid next year.
Horner told Sky Sports F1: “Well look, those tests have been planned for some time, so not something that have just sprung up. They’ve been planned for a couple of months now.
“Liam is our test and reserve driver, that’s his job.
“But I think Checo, it’s been a horrible weekend for him. We took some risks, we went for a set of inters with the first bit of rain, expecting a bit more to come.
“It was one of those calls that you could either win a lot or lose a lot and unfortunately Checo lost a lot at that point. The pace just wasn’t quite there today.”