Red Bull says it will wait until the end of the 2020 season, after next week's Abu Dhabi GP, to make a final call on Alex Albon's future.
Albon's seat with the Milton Keynes-based outfit is in jeopardy as a result of the British-Thai racer underperforming teammate Max Verstappen this season.
However, Albon's podium finish in Sunday's Bahrain GP - while lucky as he benefitted from the late retirement of Racing Point's Sergio Perez - did no harm to the 24-year-old's chances of retaining his top-level drive.
"I think Alex drove a good race today," Horner said after Sunday's race. "Sergio was unlucky, Alex benefitted from his misfortune, and I think that’s what we’re needing to see from Alex.
"His recovery from Friday was strong. Obviously after the off that he had, he qualified fourth, he was there to capitalise on Sergio’s misfortune, and he’s finished on the podium.
"It’s our first double podium since Japan 2017. It’s our first podium in Bahrain since 2013. So I think today’s been a good day for Alex."
Ahead of this week's second round of racing at Sakhir, Horner reiterated that Red Bull wanted to give Albon every opportunity to retain his drive for 2021, although Perez remains the team's most likely plan B choice.
"No decision will be made until after the final race," the Briton said.
"We're giving him every opportunity, we want him to succeed. I think we've been clear with that all along and days like today help him, but there are still two further races.
"Sergio is doing the best possible job that he can to ensure that he remains under consideration, and today was Alex's good fortune with that podium.
"But Alex had a good day today, and of course there are still two further races to go."