Jack Gaughan of the Daily Mail said that while Mourinho remains under pressure ahead of Saturday's Premier League visit to Chelsea, a change in the club's structure at this point would be a "major surprise."
"It is believed executive vice-chairman Ed Woodward would be open to an internal appointment when United do eventually begin to reshape their team behind the scenes," Gaughan added.
Mourinho was critical of the business done by the Red Devils in the summer transfer window, with the Portuguese coach said to be keen to spend big money on a defender ahead of the 2018-19 campaign.
The Red Devils' squad certainly hasn't looked complete in the early weeks of the season, as they have slumped to defeats against Brighton & Hove Albion, Tottenham and West Ham United in the Premier League.
Although there are clearly major issues in the side in terms of motivation and organisation, some fresh faces in key areas certainly would have helped the team. In both full-back positions, in central defence and on the right flank the team appears especially short of high-class options.
It was reported by Ciaran Kelly of the Manchester Evening News in September that plans were being put in place to overhaul the scouting setup at Old Trafford:
Any hesitancy to appoint a new sporting director is understandable, though, especially since uncertainty lingers around the future of Mourinho.
A director of football is typically in place to not only aid in recruitment, but to also link all facets of the football club together. It's imperative they share similar philosophies with the head coach, and with Mourinho's position seemingly precarious, any appointment would be a challenge with the long-term in mind.
Journalist Liam Canning thinks that type of figure would at least bring some much-needed order to the team:
United are entering a crucial spell of the season, with Chelsea to come on Saturday before a meeting with Juventus in the UEFA Champions League on Tuesday.
After this testing run of fixtures, Mourinho's position will most likely become a lot clearer, and perhaps then the club can start making more significant strides when it comes to any potential search for a sporting director.