"Red Bull has never had an option to buy Arrows and this latest story is a re-hash of old speculation," said Walkinshaw, who took over the team in March 1996.
The Austrian marketing man behind Red Bull, Dietrich Mateschitz, said earlier this week that he owned a majority option on the team which he aimed to exercise as soon as this month to turn Arrows into the new "Red Bull All-America Team".
Mateschitz currently owns a 64 percent stake in the Sauber team, and he is reportedly seeking to sell it for an estimated $33 million (B36m).
