According to Hitflix, director Darren Aronofsky (PI) says that his Wolverine film is not a sequel to X-MEN ORIGINS: WOLVERINE.
His film will apparently be called THE WOLVERINE, with no number or subtitle. Though it still stars Hugh Jackman, Aronofsky calls it a “one-off”, and the article implies that the intent is the seperate the production from what has come before.
My general impression was that the film was more in the line of a prequel, or falling between events shown in the last film. Its reported Japanese setting, and various plot hints suggest to comic fans that it will be inspired by the 1982 Wolverine limited series by Chris Claremont and Frank Miller.