Reeves, who is currently working on The Invisible Woman, is in discussions with producer JJ Abrams and writer Drew Goddard about a follow-up to the monster movie, according to Variety.
Cloverfield took $46 million [£23 million] in its opening weekend and Paramount is reportedly keen to repeat its success with a second film.
Reeves had previously hinted that he would like to create a sequel, but added that they would need a "compelling reason" to produce it.
