The 19-year-old, who currently has a release clause of €60 million (£52 million) in his contract, broke into his club’s senior team at the start of the year.
The Guardian believe that Manchester City are considering an offer for the defensive midfielder after sending scouts to watch him in action.
The Portugal Under-20 international has been identified as a potential long-term replacement for Fernandinho, who is approaching his 34th birthday.
However, Benfica are understood to be hopeful that Luis will put pen to paper on a new contract soon that includes an increased release clause of €100 million (£86 million).
Paris Saint-Germain have already failed with a bid for the midfielder, who has scored one goal in seven league appearances for Benfica this season.
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