Alpha Tauri team principal Franz Tost says he has been assured by parent company Red Bull that it will not sell its second Formula 1 team.
Tost said Red Bull management had assured him "that the shareholders will not sell" Alpha Tauri.
"Red Bull will continue supporting the team in the future," he said.
Tost, who has run the team since Red Bull acquired it in 2005, added: "All these rumours have no foundation."
He said the assurances had come from Oliver Mintzlaff, Red Bull's chief executive officer of corporate projects and new investments.
The 47-year-old, the former CEO of Red Bull's RB Leipzig football team, is the executive in charge of the company's F1 programme, following the death last October of Red Bull co-owner Dietrich Mateschitz.
Tost did not address one of the two central claims in the report by Germany's Auto Motor Und Sport last week, that the team could be moved to the UK.
The report said that Red Bull had concluded that Alpha Tauri, which finished ninth in the championship last year while Red Bull won a title double, was costing more than the main team.
And it said that the current organisational model, with an aerodynamic department in Bicester in Oxfordshire, and a headquarters in Faenza in Italy, was inefficient.
It said one option being considered was to move the team to England so it was closer to Red Bull's campus in Milton Keynes.
In the event of a sale, the report named three possible buyers - the US-based Andretti organisation, the British Hitech company that was associated with Russian billionaire Dmitry Mazepin, who had to step back from his position following the outbreak of Russia's war in Ukraine, and an Indian team, the Mumbai Falcons.