0744 GMT August 19, 2018
The new position will act as a "buffer" between the manager and club hierarchy, The Sun reported.
United has never previously had the role in its 140-year history.
The vacancy will be created as soon as the current restructure of the club and expansion of facilities are complete.
Mourinho said after the 2-1 win over Leicester that managers should be called "head coaches" in reference to the nightmare trying to sign players this summer.
United sees a director of football as a more permanent role against that of manager, with bosses being hired and fired frequently.
Mourinho was desperate to sign a center-back in the window but failed with moves for Harry Maguire, Jerome Boateng, Toby Alderweireld and Raphael Varane.
The United board, led by Ed Woodward, were reportedly not prepared to sanction moves for players Mourinho wanted because they thought they were too expensive.
Woodward will still have a big part to play in recruitment.
The report claims it is unclear how Mourinho might react if a director of football is appointed during his tenure.
He said after goals from Paul Pogba and Luke Shaw secured a season-opening win, "I had my plans for many months and I find myself with the market closed in a situation I did not think I would be in.
"I think football is changing and managers should be called head coaches."