Red Bull say Pierre Gasly “desperately” needs to improve his performance in the second half of the season.
The Frenchman finished sixth in Hungary on Sunday and was lapped by team-mate Max Verstappen, who finished second.
“We desperately need him realising more of the potential of the car.”
Asked whether Red Bull may need to replace Gasly, Horner said: “Our intention is to leave him in the car to the end of the year.”
Hungary was the second time in four races that Verstappen – who lost out at the Hungaroring to Mercedes’ Lewis Hamilton – has lapped Gasly, as it also happened when the Dutchman won in Austria at the end of June.
But although Verstappen was a minute ahead of the Ferraris before a late pit stop to fit fresh tyres and take the point for fastest lap, Gasly was behind both – and was also beaten by McLaren’s Carlos Sainz.
Gasly’s lack of performance also limited Red Bull’s strategic options in the fight with Hamilton – it meant the gap behind the two leaders was so big that the British driver had a more-than-sufficient gap to make the ‘free’ pit stop for fresh tyres that ultimately won him the race.
Had Gasly or the Ferraris been within 20 seconds of the leaders, that would not have been an option.
Horner said: “It’s been been a frustrating weekend for Pierre. The start wasn’t great, the first lap wasn’t great and we shouldn’t be racing Saubers [Alfa Romeos] and McLarens. We need him to be racing Ferraris and Mercedes.
“Everything we can do to try and help him achieve that is what we’ll do.”
He added: “It is vital for us, if we’re to stand any chance of catching Ferrari, that we have him finishing further ahead.
“The problem is he’s not in the mix at all. So it’s not like if LeWIS pitted he was going to come out behind him or anything like that. But [in Hungary] both Mercedes and Red Bull had ‘one-legged’ races with the team-mates out of contention.”
Who could replace Gasly?
Red Bull are notoriously ruthless with drivers who do not perform to the required standard and Horner’s lukewarm endorsement suggests there is still a chance Gasly could be dropped before the end of the season.
But the difficulty for Red Bull is the lack of obvious candidates to replace him.
Russian Daniil Kvyat is experienced, but he has already raced for Red Bull and was dropped after four races of his second season in 2016 and replaced by Verstappen.
But he has put in solid performances on his return, and scored an unlikely podium in the wet in Germany last month.
The other Toro Rosso driver is Anglo-Thai Alexander Albon, who has impressed in his debut season this year by already performing at Kvyat’s level – and sometimes ahead.
Albon has obvious potential but Red Bull would almost certainly think it was too early to promote him before the end of this season – and perhaps even as early as next year.
Last month, Horner said of Albon: “He’s doing a good job. He’s raw and he needs time. But I think he’s genuinely doing a pretty decent job in his rookie season.”
Beyond that, they would have to look to an experienced driver from another team, but that would probably have to wait until next season.