The Love Actually director wants Cruise to take the role of a vain movie star after being impressed by his performance in sports drama Jerry Maguire.
A source told the Daily Express: "If Curtis gets his way Cruise will play the part of a shallow, self-obsessed superstar who changes his ways after falling in love with a respected Chinese actress."
Hugh Jackman is believed to be the second choice to appear in the movie, which will be directed by Susanna Bier (Things We Lost In The Fire) from Curtis' own script.
Universal bosses are reportedly keen for Lust, Caution star Tang Wei to play the Chinese actress.
It was recently reported that Curtis is planning to make a film about a pirate radio station.