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Rex Features
The pair are said to have made the agreement at Ritchie's Punch Bowl pub in Mayfair on Monday night, The Sun reports.
Ritchie is reportedly currently working on remakes of musical Guys And Dolls and war movie Wild Geese.
A source said: "Work is really taking off for Guy at the moment and he is lining up talent for projects in the pipeline.
"Guy and Justin have known each other for a while through Guy's ex-missus Madonna. Guy rates Justin as an actor. He thought he was impressive in Alpha Dog. He likes his personality."
Alpha Dog was a 2006 movie directed by Nick Cassavetes which starred Timberlake as gang member Frankie Ballenbacher.
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