Horner told reporters after the sprint race that speculation about Perez's future was nothing but "noise", even if it had affected 'Checo'.
"It's only noise on the outside; on the inside everything's always clear," Horner said. "I am absolutely confident and clear that Checo will be our driver next year."
Perez had shrugged off the chatter on Thursday when he said: "I've been in the sport for 13 years and I know that everyone has a different agenda here, even the journalists, so I'm used to it."
Perez finished third in the standalone sprint, his first top-three finish in any race since the Italian Grand Prix in September, but will start ninth in Sunday's main event after a yellow flag disrupted his flying lap in qualifying.
"A really great confidence boost for him. A really strong drive," said Horner.
While teammate Max Verstappen (26) has dominated the season, securing his third world title in Qatar last month with five rounds to spare and winning 16 of 19 races so far, Perez has scored less than half the Dutch driver's points.
He is also fighting Mercedes's Lewis Hamilton (38) for second place in the championship.
Horner said he was sure the rumour-mill had affected Perez "but one of his strengths is that he has a very thick skin".
"Many times he's picked himself up, brushed himself and got back up again. So hopefully he's doing the same now."
Perez's recent form includes retiring from the Japanese Grand Prix, where he collided with Haas's Kevin Magnussen (31), and crashing at the first corner in his home race last week.
On Saturday, Perez dropped from third to fifth on the opening lap but fought back to regain the positions from Mercedes's George Russell (25) and Hamilton.
"I think he's focusing more on the basics and I think that's coming together for him," Horner said.
