ESPN says United have identified the defensive midfielder as someone who could aid Ole Gunnar Solskjaer's side.
The 20-year-old's agent, Bruno Carvalho Santos, met with club officials in January and has been dealing with enquiries since.
Nicknamed 'the Octopus' for his ability to cover the ground and win the ball in midfield, Luis has a number of reported European suitors including AC Milan, Bayer Leverkusen and Real Betis. United's rivals Leeds are also reported to have shown an interest in him.
The Portugal Under 20 international has a contract until 2024 but it is claimed Benfica are open to letting him leave on loan with the view of making that permanent.