United attempted to sign Luis in the January transfer window, with left-back thought to be a priority for David Moyes.
Current first-choice Patrice Evra looks set to leave the club at the season as his United contract expires this summer.
And his back-up, 2012 summer signing Alexander Buttner, has failed to impress Moyes in his limited opportunities to date.
As a result, the United boss has been linked with a number of defenders, notably Everton's Leighton Baines and Southampton's Luke Shaw.
But Luis is another name reportedly under consideration at Old Trafford. Big spending French club Monaco are also interested in the Brazilian international.
The report claims Atletico Madrid will demand at least £20m for Luis, but United will have no problem matching that this summer.
This week United executive chairman Ed Woodward confirmed that David Moyes will have significant funds to strengthen the squad this summer.
It's expected to be a transitional offseason this year for United, with Woodward also admitting that several first-team stars could move on at the end of the current campaign.
Club captain Nemanja Vidic has already revealed this season will be his last at Old Trafford.