The singer is said to want the pair to play King Edward VIII and Wallis Simpson, the American divorcée for whom he abdicated the throne in 1936, The Sun reports.
Madonna is believed to be producing and directing Wallis and has reportedly already met with Tennant to discuss the possibility of him starring in the film.
A source said: "The final script is now written and the locations have been scouted. Madonna is now trying to assemble the cast and put the finances in place.
"The first scene of the film is an old woman in her nineties living on her own in a Parisian flat. She starts to tell her life story to her housekeeper. It turns out the old woman is Wallis Simpson."
They added: "There will be a song for each decade of her life."
Earlier this year, it was claimed that Madonna had written to the Queen to ask for her permission to make the movie.