Long-serving team principal Christian Horner reportedly wants to be given a promotion to become the CEO of Red Bull GmbH.
It is also claimed that Alex Albon would be a top candidate to replace Max Verstappen if the three-time world champion were to leave.
Horner was last month cleared by an independent investigation following allegations of inappropriate behaviour towards a female colleague.
The 50-year-old has denied all the accusations against him and the accuser has since been suspended by Red Bull.
Christian Horner is reportedly eyeing a promotion at Red Bull
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Horner has overseen a successful start to the 2024 season on the track, with Verstappen winning both races and team-mate Sergio Perez in second.
However, the saga surrounding the team principal has clouded the start of the campaign and he has faced calls to resign from his position.
But it appears Horner has no intention to leave Red Bull, with German outlet Bild claiming he has set his sights on a new role.
The report says Horner wants to become CEO of Red Bull GmbH, a position currently held by former RB Leipzig sporting director Oliver Mintzlaff.
It is claimed that Horner is close with the company's majority shareholder Chalerm Yoovidhya.
The prospect of a Thai world champion would be attractive to Thai businessman Yoovidhya.
Bild therefore state that Williams' Thai-British driver Albon is the 'successor in sight' for Horner if Verstappen were to leave.
Verstappen's future at Red Bull has been thrown into doubt following a falling out between his father, Jos, and Horner.
Jos Verstappen has called for Horner to resign from his position on more than one occasion in the wake of the investigation.
Verstappen junior has been linked with a move to Mercedes to replace the Ferrari-bound Lewis Hamilton.
And former F1 driver Johnny Herbert claims a deal is already close with the Silver Arrows.
Herbert told The Sun: "It's not a good thing for F1 with the whole thing going on and the belated heat on it.
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Alex Albon is said to be a leading candidate to replace Max Verstappen if he left Red Bull
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"It doesn't help the situation for Red Bull who have the best driver in the world at the present time.
"And they're very close to pushing [Max Verstappen] out of the team, I've heard they are getting quite close with the deal with Mercedes.
"It seems like a stupid thing to do, their biggest asset is not the Christian Horner show."
Herbert has also joined the calls for Horner to resign from his role at Red Bull.
Max Verstappen could leave Red Bull to join Mercedes in 2025
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He added: "It's the impact, the possible destroying of the team and the success they have had.
"It's not about the Christian Horner show, it's about the Max Verstappen show as he is the one winning all these races and championships for Red Bull.
"It would be crazy for Max to leave because of the situation...Jos has said it will be very destructive and rip it apart and I think it's gone on for far too long.
"In some respects, Christian should really think about it and step aside."
