Mangold, who helmed Tom Cruise and Cameron Diaz's action comedy Knight and Day last year, has been approached by studio Twentieth Century Fox, according to Deadline. He is reportedly also Hugh Jackman's first choice for the role.
His previous directorial credits also include Walk the Line and Girl, Interrupted.
Mangold appeared on a shortlist of candidates which was reported across the press last month.
The list also included Fast and Furious 5 director Justin Lin and The Bourne Identity's Doug Liman.
Black Swan director Darren Aronofsky was attached to the The Wolverine but stepped down in March, saying that he did not wish to spend a prolonged period of time away from his family.
Mark Romanek told Digital Spy that he would not be helming the film earlier this month, saying that the script "didn't seem like my kind of thing" and was "not something I felt really passionate about".
Valkyrie writer Christopher McQuarrie has penned the screenplay, which reportedly focuses on Wolverine's time in Japan.
The Wolverine, which is the follow-up to 2009's X-Men Origins: Wolverine, has not yet officially been greenlit. It was originally scheduled for release in 2012.
Watch the trailer for X-Men Origins: Wolverine below: