Slated to start shooting in Budapest in April with McG at the helm, "Terminator Salvation: The Future Begins" would be the fourth film in the series and is set for a summer 2009 release.
The character of hero John Connor was played in previous "Terminator" outings by Nick Stahl and Edward Furlong.
The fourth "Terminator" adventure is scheduled to come out a year after Bale will be seen reprising his role of Batman in "The Dark Knight," the trade paper said.
Both films are Warner Bros. projects.
It is not clear whether California Gov. Arnold Schwarzenegger, star of the first three movies, will appear in the new "Terminator" installment.