A recent report in Germany's Auto Motor und Sport said Red Bull might seek to move AlphaTauri from Italy to England or sell the team, with American Michael Andretti talked of as a possible purchaser.
Red Bull founder Dietrich Mateschitz was a supporter of both teams but the Austrian died last October and Oliver Mintzlaff has since taken charge of sporting projects.
"I had some very good meetings with Oliver Mintzlaff, who confirmed that the shareholders will not sell Scuderia AlphaTauri, and that Red Bull will continue supporting the team in the future," Tost said in a statement ahead of the season-opening Bahrain Grand Prix.
"All these rumours have no foundation, and the team has to remain focused for the start of the season to perform better than last year."
AlphaTauri finished ninth of 10 last season.
They have a changed lineup, with Japan's Yuki Tsunoda (22) partnered by new Dutch driver and former Formula E champion Nyck de Vries (28).
