Villa are looking to fill a vacancy after chairman Doug Ellis decided to stand down as chief executive.
But Birch said: "The reports about me having agreed to join Villa are wrong. People are jumping the gun. I am keeping my options open."
A Villa spokesman said: "The search for a chief executive is continuing. No decisions have been reached."
Birch has been constantly linked with a move to Villa and was a target before he joined Leeds to guide them through their financial crisis.