The test reportedly took place at the Austrian automotive company AVL's 'rolling road' facility in Graz, involving Red Bull's troubled engine supplier Renault.
But late on Thursday, the reigning world champion team denied conducting the test.
Red Bull, however, pointed out: "The test mentioned in the article would be permitted by the regulations".
Germany's Auto Bild appears to have got to the bottom of the story.
The publication said the story broke when an anonymous person wrote letters to rival teams Ferrari, Mercedes and Sauber, as well as the governing FIA.
"Auto Bild Motorsport knows that a Toro Rosso chassis without front and rear wings ran on the 'rolling road' without a flow of (wind tunnel) air.
"Therefore, the test was bench testing and completely legal. The identity of the anonymous letter writer remains," the report added.
Toro Rosso and Renault did not comment.