Red Bull team chief Christian Horner and his lead driver Max Verstappen on Friday both told Pierre Gasly to stay put at AlphaTauri and not seek a return to the senior outfit.
Since winning at Monza last week, Gasly has said he was ambitious to join a leading team, including Red Bull who demoted him a year ago.
Speaking ahead of the Tuscan Grand Prix at Mugello this weekend, Horner suggested a return to Red Bull made little sense because he sees AlphaTauri, which changed its name from Toro Rosso for this season, "as a sister team rather than a junior team".
"AlphaTauri is a rebranded team for this year," said Horner. "I think their aspirations are beyond Toro Rosso's," Horner said.
Verstappen, Red Bull's number one driver, warned Gasly that returning was a bad idea.
"Anyone can come back and try again," said the Dutchman, who out-classed Gasly in the first half of 2019 and has generally done the same to replacement Alex Albon this season. "But they will not succeed."
Horner said Red Bull did not intend to give up on Albon.
"I think that as far as Red Bull Racing's seats are concerned we're focussed on Alex Albon, we want to try to give him the best opportunity to retain that seat," Horner said.
"Pierre has done a fantastic job," added Horner. "Since taking a step back into what was Toro Rosso, now AlphaTauri, he's found his confidence, he's driving incredibly well.
"AlphaTauri are doing a great job with him. It's really good to see that's working out for him."
Horner added that there were other reasons why he did not favour an early swop.
"We've got some issues that we're working on with the car. I think that it wouldn't make sense to switch the drivers back."
Alpha Tauri team chief Franz Tost said he expected a decision on the make-up of the two teams before the end of the season.
"The driver question will come up with Red Bull at the end of October, beginning of November," said Tost. "We'll see how everything is continuing and then Red Bull makes a decision, which driver is racing in which team."
"I rate him very high because what he showed in Monza he is really a fantastic racer... He drove, I must say, a very, very mature race."
Red Bull is based in England and AlphaTauri in Italy but, said Horner, they were going to share more technology.
"We have a synergy project within the regulations," Horner said. "AlphaTauri will be utilising the same equipment, the same wind tunnel, and of course that will hopefully be helpful to them in their development."