Producer Barbara Broccoli offered Craig, 37, a three-film deal, estimated to be worth nearly $30 million over the next 10 years, the Guardian said Wednesday.
The Sun newspaper said Broccoli's preferences centered on Craig and Clive Owen, who reportedly was not interested.
Craig has recently gained fame for his roles as a middle-rank gangster in "Layer Cake" and the rational journalist driven to the end of his tether in "Enduring Love."
TV viewers may also have seen Craig as Fluke Kelso in the small-screen adaptation of Robert Harris's "Archangel" just a couple of weeks ago.
Celebrity Families of 2014 [PHOTOS]