As reported by talkSPORT, United failed with a £16.6m offer for the left-back - and the report claims the player had no interest in the move anyway.
United boss David Moyes has been linked with a number of full-backs as he looks for a long-term replacement for Patrice Evra.
The French international is out of contract at the end of the season and looks likely to leave.
Leighton Baines and Luke Shaw have been mentioned as possible targets, as well as Real Madrid's Fabio Coentrao.
But United reportedly attempted to lure Luis to Old Trafford with an offer for the Brazil international.
The 28-year-old did not consider leaving as he's happy at the Vicente Calderon. And why wouldn't he be - Atletico Madrid are flying high in La Liga and have a shot at a first title since 1996.
United face a real battle to even qualify for the Champions League this season - following their 2-2 home draw against Fulham on Sunday David Moyes's side sit seventh in the Premier League, nine points behind fourth-placed Liverpool.