The blockbuster will be directed by Gareth Edwards, who previously worked with McNairy (Killing Them Softly) on sci-fi indie film Monsters.
Joseph Gordon-Levitt was also reportedly in the running to star in Godzilla, but turned down an approach late last year.
According to Variety journalist Justin Kroll, Gordon-Levitt and Cavill are studio choices, while McNairy and Landry Jones are favoured by the production's creative team.
It was confirmed earlier this week that Frank Darabont (The Shawshank Redemption, The Walking Dead) has been hired to deliver the final rewrite on Max Borenstein's script.
The story was also re-written by Iron Man 3 scribe Drew Pearce.
Godzilla will be released on May 16, 2014 in direct competition with Ninja Turtles, Michael Bay's movie reboot of the comic book franchise.
Watch a trailer for the 1998 Godzilla movie below: