Dr Helmut Marko says Red Bull has "no intention" of axing Pierre Gasly.
Franz Tost, the Toro Rosso boss, told the German podcast meinsportpodcast that Daniil Kvyat would make a good replacement.
"I don't think Red Bull would lose face by taking him back," he said.
But at a pre-Austrian GP event in Graz, Marko said Red Bull is determined to keep trying to get Frenchman Gasly up to speed.
"He's working hard with the team, which is why he is in the simulator today and not here," said the Red Bull official.
"We have no intention of changing him. Gasly is working with a young race engineer which certainly didn't help, and he lost a lot of confidence with the two accidents in Barcelona.
"But he has also had some strong races. We will work together to bring him forward," Marko added.
However, Marko said Red Bull will turn its attention to the identity of Verstappen's teammate for 2019 in "September or October".
He played down suggestions Sebastian Vettel could return to Red Bull from Ferrari.
"As you know, nothing is impossible in Formula 1," Marko said.
"But Sebastian has a contract with Ferrari in 2020."
Finally, Marko named the teams that are blocking the resurrection of Pirelli's 2018 tyres, as he claims the current design only favours Mercedes.
"Six teams want the change and Pirelli could do it in a few weeks. But four teams - the three Mercedes teams and McLaren - are against it," said Marko.body check tags ::