Ricciardo previously raced alongside Max Verstappen at Red Bull between 2014 and 2018, clinching seven race wins in that time, before going on to experience disappointing stints at Renault and McLaren.
The Australian rejoined Horner's team as a third driver following the mutual termination of his McLaren contract in 2022, before making his comeback to the track midway through the 2023 campaign, replacing Nyck de Vries at Alpha Tauri (now RB).
Despite hopes that the 34-year-old could rediscover the form which had previously made him such a sought-after talent, performances have been largely underwhelming, leading to speculation that he is under pressure to retain his seat.
Speaking ahead of last weekend's Chinese Grand Prix, Horner said Ricciardo must show significant improvements if he is to stand any chance of a sensational return to Red Bull in the future.
"He needs to show the kind of head-turning form to make not only ourselves, but potentially to make others take notice."
He went on to confirm that RB's reserve driver, Liam Lawson is eager to get going in F1, and that the 22-year-old New Zealander could soon be ready to make the step up.
"Now, obviously, waiting in the wings is a driver with the talent of Liam Lawson, who naturally is champing at the bit to get an opportunity," Horner continued.
"But there's nothing pre-set of preordained as to when or even if that would take place.
"The priority is for sure the drivers that are in the race seats at the moment and we'll see how that pans out."