The Blues are already nearing a deal for the Rojiblancos’ prolific striker Diego Costa, and are now also chasing his team-mate from their impressive 2013/14 campaign.
Luis was one of the star’s of Atleti’s campaign, and was an ever-present as they lifted the La Liga title and ended the Champions League as runners-up.
Chelsea are known to be in the market for a new left-back after releasing Ashley Cole, and the Brazilian is in line to fill the void.
It is understood that the Londoners have informed the Madrid side that they will pay the defender’s £20m release clause, which will leave them free to thrash out a deal with the 28-year-old.
Luis himself is thought to be keen on the switch, so it would appear likely that a move will go ahead.
Costa is also expected to make a £35m switch to Stamford Bridge to follow fellow Spaniard Cesc Fabregas in a massive overhaul at the club.
Much of the cash for the transfers will come from the sales of David Luiz, Kevin De Bruyne and Juan Mata, which have brought in over £90m since January.