Mr Mitchell was forced to resign last year over claims he swore at police officers and called them "plebs" after they refused to allow him to cycle through the main gates of Downing Street.
But after evidence emerged casting doubt on the police account, a newspaper reported Mr Cameron had offered him the EU post when Baroness Ashton finishes her term as foreign affairs envoy next year.
The offer was said to have been made over a lunch with Mr Cameron and his wife Samantha at the Prime Minister's official country residence at Chequers – a signal of Mr Mitchell's political rehabilitation by No 10.
In a TV interview Mr Mitchell confirmed he had met Mr Cameron. He said: "There is a very important job to be done in Europe to make sure that Europe changes in the interests of everyone in Europe but also in the interests of Britain."