United spent big in the summer when bringing the likes of Harry Maguire to the club, but Ole Gunnar Solskjaer's rebuilding job is far from over and attention is already being turned to the January window.
The Reds boss is said to be in the hunt for a new defensive midfielder, and reports are rife suggesting that Luis is high on his wanted list as he continues to shine for the Portuguese side.
Luis is just 20 years of age and fits the profile of the kind of player that Solskjaer is looking to bring to United, but he is not alone in his admiration.
City were reported to be weighing up a move for the youngster in the summer, but snapped up Rodri instead, while Paris Saint-Germain are also said to be keen.
The interest in him will hot up even further if Benfica give any encouragement to interested parties, so United would have to move quickly if they wish to wrap up a deal.
United scouts were said to be in attendance as Benfica hammered Braga 4-0 last Sunday, and Luis was one of the players under the microscope.
The other is said to central defender Ruben Dias, so there is every chance a double swoop could be on the cards.
Luis will be a key player for Benfica this season and has already started five games, so they will be very reluctant to let him go.
If they do, then it is unlikely such a big transfer would happen in January and United may have to wait until the end of the season.
The player currently has a £91million release clause in his contract, but Benfica are keen to get him tied down to a fresh deal so they can increase it further.