The Champions League finalists have confirmed the arrival of Guilherme Siqueira on a four-year deal from Granada in a deal worth around €8 million.
That clears the way for Chelsea to wrap up a deal for Luis, who will arrive at Stamford Bridge as the replacement for the out-going Ashely Cole.
Luis has a €25 million release clause written into his contract which Chelsea are expected to meet, having already coughed up £32 million in order to land forward Diego Costa.
Former Chelsea midfielder Tiago, who is out of contract at the Vicente Calderon this summer, is also believed to be on his way to Stamford Bridge.
With Thibaut Courtois on his way back from loan with Atletico Madrid, Chelsea could have four of the players who featured for Diego Simeone's side in their Champions League final defeat against Real Madrid last month.
‘Siqueira will increase the competitiveness of the group,’ Madrid's sports director Jose Luis Perez Caminero said of his team's new arrival.
"He is a player that is very strong at set-plays, taking penalties, he has a lot of attacking qualities as well as great defensive ability."
Chelsea are also on the verge of wrapping up a deal for Barcelona midfielder Cesc Fabregas.