Citing reports from Spain, the article claims Chelsea boss Jose Mourinho is eyeing up United target Luis as a long-term replacement for 33-year-old Ashley Cole.
The England international has not featured for Chelsea in recent months, and could leave the club for free this summer when his contract expires.
Cesar Azpilicueta has won praise from Mourinho for his performances at left-back, but the Spaniard is not viewed as the answer going forward for the Blues.
Luis meanwhile, has been one of Atletico’s standout players this season as Diego Simeone’s men challenge for a La Liga title.
The Brazilian full-back has been tracked by United scouts, and it seems Chelsea are now also keeping a close eye on him. United are actually in a similar situation to Chelsea, with long-term starter Patrice Evra out of contract at the end of the season.
The report claims Atletico Madrid would look for at least £20m for Luis, especially considering big-spending Monaco are also reportedly interested in him.
Similarly, Diego Costa is thought to have a release clause in his Atletico contract that allows him to talk to other clubs if a bid of £32m is made.
Chelsea scouts would have left impressed from their trip to Spain to watch the duo last week, as Atletico ran out 4-1 winners over AC Milan to reach the quarter-finals of the Champions League.