The idea of a cameo was apparently brought up when the prince visited the film set recently and posed for photos with Craig.
Now, the source says the 70-year-old is "considering it".
If he turns it down, the source says his sons, Princes Harry and William, "could be in producers' sights next",
The princes both filmed cameos for 2017's Star Wars: The Last Jedi where they played stormtroopers, but they were ultimately cut from the film because they were too tall and stood out.
Bond 25 has been hit by a plague of issues during filming including director Danny Boyle quitting, an explosion on set and Craig needing surgery for an ankle injury.
The source told The Sun: "It is no secret that the film has suffered a number of setbacks but landing a Royal could be just what the movie needs."