The flamboyant Brazilian defender has fallen out of favour at Stamford Bridge after a bust up with coach Antonio Conte, with their relationship still not fully healed.
Arsenal manager Arsene Wenger is looking for reinforcements to his leaky defence in the January transfer window, and Express Sport understands that Luiz, 30, has shot to the top of the list of prospective candidates.
Luiz is also a target for Manchester United manager Jose Mourinho but a host of other clubs have been linked with the Brazilian international, including Juventus and Real Madrid.
What appeals to Wenger is that Luiz can play either as a centre back or defensive midfielder, has extensive Premier and Champions League experience and could slot straight into his team.
Luiz has had meetings with Conte to try and resolve their differences since being dropped following a row after the 3-0 Champions League defeat at Roma.
The Chelsea manager has said he wants the Brazilian back in his side but Luiz has demanded regular first-team football.
Luiz has played just once since being dropped for the win over Manchester United – against outsiders FC Qarabag in the Champions League.
He then sustained a knee injury which has kept him out for a month but sources close to the player insist he is now near to full fitness.
However, Luiz’s place in the Chelsea side now appears to have been taken by talented young Danish defender Andreas Christensen, who Chelsea are planning to hand an improved contract to in the new year.
When asked about Luiz’s future at the club, Conte said last week: “I don’t know. Andreas Christensen is the present and future for Chelsea.”
Christensen, 21, has developed into a key figure in Conte’s plans this season, after spending the previous two campaigns on loan at Borussia Monchengladbach.
The young Denmark international defender’s current contract runs out in 2020, but the club want to secure his future long term.
Talks on new deals for key forward Eden Hazard and goalkeeper Thibaut Courtois are also expected to be made a priority early next year.
Chelsea’s loan technical coach Eddie Newton said: “Andreas is a player that we can definitely have here for the next 10 years. He is another John Terry for me, and has that same kind of stature because he has got that ability.
“This season, he stepped in against Tottenham and Manchester United and it was like he has been there all his life. He is an incredible footballer and one this club should keep hold of very tightly.”
Alex Iwobi contract
Meanwhile, Arsenal will also open talks with Nigerian forward Alex Iwobi in the New Year.
The 21 year old has three years left on his current £30,000 a year deal, but Wenger wants to secure the future of a young player who has made himself an important part of his plans.
Theo Walcott will come out of the shadows to feature in tonight’s Carabao Cup quarter final against West Ham at the Emirates.
Walcott has yet to start a league game for the Gunners this season, his only openings coming in the Carabao Cup and Europa League.
Wenger is expected to make changes for the tie, with both Aaron Ramsey and Shkodran Mustafi still out injured.
The Gunners boss said: “We have so many quality players who did not start on Saturday. The players who will start are basically all international players, so that is why the squad rotation makes sense. We have to show the trust and confidence in the players who did not start last week.