The James Bond actor joins Ewan McGregor, Orlando Bloom and Tom Hardy in expressing "huge interest" for the adaptation of ITV's classic 1970s cop show, says the News of the World.
Ray Winstone is rumoured to have been cast as Regan, who was originally played by Inspector Morse actor John Thaw.
"All four are keen on the role but whoever ends up doing it will change the movie's tone. Ray's going to be great as Regan but the chemistry between him and Carter needs to be right," a source said.
"The success of Life On Mars shows there's a huge appetite for '70s cop dramas. With the right cast The Sweeney could be even bigger."