According to journalist Duncan Castles, Mourinho has told Woodward he is willing to have someone work above him to be in charge of transfers.
However, Mourinho has demanded that must be someone he approves.
That man could be Lille’s sporting director Luis Campos, who was a scout at Real Madrid during Mourinho’s time at the Bernabeu.
And, if Campos does arrive at Old Trafford, Mourinho could lean on his support in a bid to bring Napoli centre-back Kalidou Koulibaly to the club.
“Mourinho is obviously cautious about having a director of football brought in above his head, who would have the authority to sign players and who might recruit players he doesn’t want,” Castles told The Transfer Window podcast.
“He doesn’t want to be working with someone he doesn’t trust in that position.
“He’s not against the idea of a director of football in principle.
“In fact, he thinks it could be helpful to have an ally in the camp – or at least someone to take some of the heavy load away in terms of the search for players, in terms of recommending players to the board, in terms of arguing with the board that this particular signing, for example Koulibaly, is the right one at this particular moment.
“I think it should be noted here that Mourinho lost his assistant coach Rui Faria in the summer and the number of trusted individuals who he’s worked with for a long period of his career has reduced and that’s made his job more difficult at United.
“But his proposition – and he’s talked to Woodward about this – is, if it’s a director of football it has to be someone that I approve of and I’m comfortable working with.
“Luis Campos is the clear candidate there, because Mourinho hired Campos as the technical and tactical and also a scout to look for players at Real Madrid and was pleased with his work there.”
United are in action this weekend against Crystal Palace as Mourinho seeks a fresh start following the loss to Manchester City before the international break.
The Red Devils then face a crunch Champions League tie with Young Boys on Tuesday, where a win would put them in the driving seat to qualify for the knockout stage.
Mourinho’s men also face Arsenal and Liverpool before Christmas as the Portuguese boss seeks to recoup ground on their Premier League title rivals.
City, Chelsea and Liverpool are all yet to lose a game in the top flight this season.
United start the weekend in eighth place – a staggering 12 points off table-toppers City.