Nope. It could never work. The film was based on a popular book and director Francis Ford Coppola was able to do something that NOBODY thought could ever be done -- make a film that was better than the book, and turn it into a box office blockbuster and Academy Award winning film. And it starred an already legendary actor (Marlon Brando), and a young cast that would soon become Oscar winning or nominated stars (Al Pacino, Robert Duval, James Caan, Talia Shire, John Cazale, Diane Keaton, and from Part 2, Robert DeNiro, Michael V. Gazzo, and legendary acting teacher, Lee Strasberg).
Parts 1 and 2 are already considered perfect in the film community and have legions of fans around the world, so to remake them would be considered sacrelige. And the classic 1960 film "Psycho" already was remade and failed on all fronts, so I don't think Hollywood will be jumping on the bandwagon of remaking The Godfather.
Besides, the book's author, Mario Puzo, and Francis Coppola have the rights to "The Godfather", so unless Coppola loses his mind (Puzo passed away several years ago), there is no way it could ever be done.
But I'm just interested in knowing, if you had your choice of actors, who would you choose to star in the lead roles?