United want to bring someone in to oversee transfers and are understood to be considering former Southampton and Tottenham man Paul Mitchell to fill the role.
Roma transfer supremo Monchi has also been linked with the role but it is claimed he does not want to leave Italy.
United continue to search for a suitable candidate and The Telegraph claim Mourinho is not keen to work under such constraints.
However, the Portuguese is under huge pressure because of United’s dismal start to the season and might need to bow to the board’s demands or lose his job.
They are currently languishing in sixth in the Premier League 19 points behind leaders Liverpool, who made light work of them in their 3-1 victory at Anfield on Sunday.
That is the furthest off the top they have ever been at this stage of a Premier League season.
But what will be of more concern to the board is the 11-point gap between them and fourth-placed Chelsea as they look to secure Champions League football next season.
Another route into the Champions League is by winning it this season but that looks unlikely after they were drawn against Paris Saint-Germain in the last 16.
While Mourinho is under pressure, reports suggest the club are willing to stick with him for now and he could be backed with significant funds to try and turn the situation around in the January transfer window.
However, any new signings could have to be made under the guidance of a new sporting director.
Mourinho might not like that and he has already fallen out with the board after they failed to sign a new centre-back in the summer.
The United boss wanted to bring in one of Toby Alderweireld, Harry Maguire or Jerome Boateng but the board blocked any deal as they did not believe them to be value for money or an upgrade on the players already at the club.
They are now said to be keen on following the successful model at Liverpool, whose own sporting director is responsible for recent signings such as Mohamed Salah, Roberto Firmino, Sadio Mane and Alisson.
While United have resisted the chance to go down that route in the past, The Telegraph says they are worried about being out of touch with their more forward-thinking rivals.
If the appointment is made, it will be the first in the club’s history.