Deadline claims that both Paramount Pictures and series star Tom Cruise want the Way of the Gun filmmaker to helm the proposed sequel.
[Left: Christopher McQuarrie / Right: Tom Cruise]
Cruise recently worked with the director on the forthcoming Jack Reacher, as well as Valkyrie, which McQuarrie wrote.
McQuarrie has prior experience with the Mission: Impossible franchise, having provided script revisions for the fourth instalment, Mission: Impossible - Ghost Protocol.
Cruise, who has a hand in producing the espionage movies, previously said that he is planning the fifth entry in the series and will continue to star in Mission: Impossible films while there is still a demand for them.
He will next appear on screen in Jack Reacher, which touches down in cinemas on December 13.
Watch a trailer for Jack Reacher below: