Manager Scott Parker wants to strengthen his options in the middle of the park and is keen on the Portuguese.
AC Milan are also interested in the services of Luis, but Fulham want to include a £27 million option to buy clause in the loan deal.
The 21-year-old is also on the radar of a number of other top European clubs despite playing just 21 games for Benfica’s first-team.
Parker wants to ensure that his side hold on to their Premier League status at the end of the campaign, and Fulham have been making some smart moves in the summer transfer window.
Leeds United have also been linked with Luis, but they haven’t made concrete moves for the youngster and it appears that their fellow newly-promoted rivals are ready to pip them to his signature.
The Portugal youth international has also been scouted by Manchester City and Manchester United, and he will be keen to prove himself in the top-flight if a move to Fulham works out.
Luis’ ability to play as a holding midfielder and in a box-to-box role will come handy at Craven Cottage, and it will be interesting to see if they can seal a move for the in-demand youngster.