The British filmmaker is keen to cast The Fall star in the leading role of King Arthur in medieval drama, Knights Of The Roundtable: King Arthur.
A source told The Sun: "Guy was completely blown away when he met him and wanted to offer him the part immediately. Jamie is keen on the role too and his US agents are keen to work out a deal where he'll be able to do both franchises."
Jamie, who is to play hunk Christian Grey in Fifty Shades Of Grey, is apparently committed to a three-film deal with Universal, the studio behind the big-screen adaptation of EL James' novels.
But the Northern Irish actor is interested in trying new roles, with the insider adding: "Jamie is keen to take on other roles and prove that he's an adaptable actor."
Idris Elba is said to be in talks to play Bedivere, Arthur's father's right-hand man, who will teach his son how to lead an army.
The film, which has been written by Joby Harold, is Warner Bros' new take on the English myth. It will tell the story of King Arthur and his knights of the kingdom of Camelot and is scheduled for release in July 2016.