Luis joined Atletico from Deportivo La Coruna in the summer of 2010, and spent four years with the Madrid club before making the move to Chelsea ahead of the 2014-15 campaign.
The Brazilian only lasted one season at Stamford Bridge, however, before sealing a return to Atletico.
The 32-year-old is still an important figure at the Spanish club, but a number of injury problems have seen Lucas Hernandez given the opportunity to impress in the left-back position this season.
According to Gazzetta dello Sport, Juventus have already held a meeting with the defender's representatives as they consider a move for a player who will be out of contract at the end of the 2018-19 campaign.
Luis has recently returned to the training field following a leg fracture.