Brosnan, 50, announced he was quitting the role this week after starring in four Bond movies.
Brosnan complained back in March that he hadn't been asked to play 007 in the 21st film.
After 20 films in the series, producers want to "modernise Bond and turn him into a youthful, suave and modern hero to compete with the likes of Spider-Man and Keanu [Reeves] in 'The Matrix'," said a source close to the project.
The beefy beat off competition from the other main contenders Jude Law and Ewan McGregor to take over the role of the super-spy in the long-running series of films.
Bana is still negotiating with the series producers but they are hopeful he will become the sixth actor to play the smooth Bond.
Bana began his career as a stand-up comedian, appearing in popular TV sketch comedy "Full Frontal" before getting his big break in the dramatic feature film about serial killer Mark Read, "Chopper".
In recent years, Bana moved to the US for starring roles in "Black Hawk Down", "Hulk" and "Troy".
If he accepts the role, Bana will be the second Australian to play Bond, after George Lazenby starred in On Her Majesty's Secret Service.
The James Bond films, based on the novels of Ian Fleming, have proved hugely successful ever since Sean Connery starred in the first Bond movie Dr No in 1962.
The next Bond film will be the 21st in the series.
