The actor told the Radio Times that he would be interested in playing the Doctor if the role fitted into his acting schedule.
"Who knows, in a couple of years, I might go down on my knees to play the Doctor," he said. "If I could do it for three months and do other stuff the rest of the year, I'd do it."
The Judge John Deed star also admitted that he had turned down the iconic role of James Bond in the late '70s.
"[Producer Barbara Broccoli] had seen me in The Professionals and begged me to do a screen test," he confirmed. "I said no for the same reason. It dominates everything you've done or go on to do. She was astonished. In retrospect, it might have been a good idea to have had a go at it."
Shaw will next be seen in the third series of Inspector George Gently, which begins September 26 on BBC One.