Luiz, 31, lost his starting spot under head coach Antonio Conte at Chelsea last season and finished the 2017-18 campaign having started just nine times in the Premier League.
Conte may depart the west London club this summer, though, per Matt Law in the Telegraph.
However, with Cesar Azpilicueta, Antonio Rudiger, Andreas Christensen and Gary Cahill all competing with Luiz for centre-back spots at Chelsea, the Brazilian still faces an uncertain future.
At Arsenal, he would have a much better chance of playing regular first-team football.
Arsenal's defence needs a serious overhaul as even Laurent Koscielny, currently sidelined through an Achilles tendon injury, showed signs of fallibility last term.
New manager Unai Emery has also worked briefly with Luiz before at Paris Saint-Germain.
The Spaniard started the defender in three Ligue 1 games at the beginning of the 2016-17 season before he returned to Chelsea in a £34 million deal.
A 56-time Brazil international, Luiz's career has been inconsistent to say the least.
Often accused of being something of a liability at the back, he was brilliant in Conte's 3-4-3 system in 2016-17 as Chelsea won the Premier League and he was included in the PFA Team of the Year.
Arsenal need composure, experience and leadership in the back line if they are to improve defensively next term—they conceded 51 times in the English top flight last season.
Luiz offers at least two of those attributes and could be worth a gamble.