According to Tony Banks of the Daily Express, the Brazilian is edging closer to the exit door at Stamford Bridge after falling out with manager Antonio Conte.
The Gunners are said to be ready to capitalise with a £30 million offer in the midseason market. Additionally, Manchester United are also reported to hold an interest in Luiz, while Juventus and Real Madrid have also been linked.
Banks noted Arsenal boss Arsene Wenger "is looking for reinforcements to his leaky defence," and Luiz appeals to him because he "can play either as a centre-back or defensive midfielder, has extensive Premier and Champions League experience and could slot straight into his team."
In the report, it's suggested the relationship between Conte and the former Paris Saint-Germain man is "not fully healed."
Links to Arsenal come as a surprise, and Gunners fan Renato was torn over the prospect of landing the Brazil international:
Looking at his form last season, that version of Luiz would make a huge difference to this Arsenal setup.
The 30-year-old has excelled at the heart of Chelsea's three-man defence. Conte gave him a straightforward brief, meaning Luiz was able to focus on his defensive duties and not worry too much about bringing the ball out of the back and distributing.
Luiz's ability to win tackles, dominate aerial battles and boss physical tussles with centre-forwards was key to the Blues being so imperious in defence. Squawka Football provided the numbers behind the defender's 2016-17 term:
It was a season that culminated in the Premier League title for Luiz and Chelsea. The current campaign has not been as prosperous for the player or the team.
In addition to the reported fallout with Conte, Luiz has been battling with various injury issues. As such, his form has been inconsistent, while in Andreas Christensen, the Blues have found an excellent alternative to the Brazilian.
It's why, if the right sort of offer were to arrive in January, you could see Chelsea deciding to do business. Dermot Corrigan of ESPN FC suggested it would be fun to see the defender at Real Madrid:
Arsenal would benefit from a quality centre-back arriving at the club, and the chance to get someone of Luiz's pedigree doesn't come around often.
Wenger's side can look secure and solid for long spells of matches, although lapses in concentration and poor choices can often cost them. A defender who dominates, leads and inspires confidence in team-mates would make the Gunners a much more formidable opponent.
Last term, Luiz was that man for Chelsea although there are doubts as to whether he could offer that type of focal point for a longer period of time. Nevertheless the Blues would surely be reluctant to sell one of their key players to a rival.