The 30-year-old actor is now considered as the overwhelming favourite to land the coveted licence to kill now that Daniel Craig has quit the role after four movies, reported Daily Mirror.
"Poldark" star Turner had recently risen to the top of many bookies' lists, but the BBC announced on Wednesday that he was on board for a third series of the historical drama, effectively removing him from the running.
While Norton may not be the biggest name in the running and his few film credits include "Mr Turner" and "An Education", as well as a number of TV roles in "War & Peace" and "Happy Valley".
Idris Elba's odds also appear to be lengthening, even though he has been touted as Craig's replacement for nearly a year.