Team-mate Daniel Ricciardo, meanwhile, has been simultaneously linked with a return to the Red Bull team and relegation to the sidelines in favour of Red Bull junior Liam Lawson.
The fluid situation has kept Bayer busy, and the 53-year-old moved to praise Ricciardo and Tsunoda when discussing their futures.
Who will drive for Red Bull in 2025?
Despite coming under intense scrutiny after a long string of weak performances, Red Bull have confirmed that Sergio Perez will remain at the team beyond the summer break.
The Mexican only signed a new contract in June, but has not vindicated that decision since and it is suggested that he could be replaced well before the expiry of his fresh deal.
Both RB drivers have been touted for this role, though Tsunoda's chances seemed to fade when he committed to RB for 2025 earlier this year. Next season will be the 24-year-old's fifth at the so-called junior team.
However, Bayer stressed that did not mean his opportunity at the senior team would never come.
“Helmut [Marko, Red Bull's motorsport advisor] said it himself, in German you say, 'a swallow doesn't make a summer',” he told Motorsport.com. “What it means is that if Yuki keeps racing on this level consistently, he will be considered for a seat in Red Bull Racing."
Bayer also praised Ricciardo, who has shown much stronger form after being comfortably beaten by his younger team-mate earlier in the season.
On promoting drivers from RB to Red Bull, he said: “That's ultimately exactly our mission and the mission we've been given by the shareholders, and if that means that he [Tsunoda] needs another season next to a very strong Daniel, that could be an option.
“It could also be an option [to] say that, okay, we now believe he's ready. So, we'll talk to Liam. We're not in a hurry, despite all the people [who] think we are, because we do have all the options in our hands.”
Lawson is an option to join both Red Bull teams in 2025, though it is more likely to be RB. Though Bayer claimed the team would take their time, Marko confirmed that Lawson's future would be announced in September.
“Yuki is a Red Bull driver," continued Bayer. "He must have the ambition to drive for Red Bull Racing. If he doesn't have that - it's wrong. I hope and I trust that he wants more than anything else to drive that car to win races. We also try to help him developing him in that way. So that's what the business is.
“Was he fully happy to extend with us to drive for us next year? Yes, it's a question for him, but because what he tells us is that he is mega ambitious, he can see a team [that] is mega ambitious and the fit is obviously working.
“It helps him develop, he has paid us back with quite [an] incredible level of performance.”
Tsunoda has amassed 22 of RB's 34 points this season, with seven grand prix points finishes to Ricciardo's three. Whether either can do enough to make the step up to Red Bull remains to be seen.