According to The Sun, the Gunners are planning to launch a £25m ($33.4m) bid for the Brazil international. The central defender is currently sidelined with a knee injury and is expected to return to action at the start of next month.
The north London club are planning a "stunning move" to convince Luiz to make a switch to the Emirates, once he returns to full training. The player is also focused on regaining fitness, amid uncertainty around his future.
Chelsea manager Antonio Conte and Luiz had a fall out over a tactical row. The report claims the relationship with the pair have improved as the Blues coach is looking to have his player back in contention for the first-team.
Luiz returned to Stamford Bridge from Paris Saint-Germain in 2016. He played a key role in the heart of the defence, helping Conte win the title in his debut season in England. He last featured for Chelsea in their 4-0 Champions League win over Qarabag.
The former Juventus and Italy manager dropped the South American defender since October. He was omitted from the squad when Chelsea managed a narrow 1-0 win over Manchester United in November.
Chelsea manager then confirmed it was a tactical decision to drop Luiz against Jose Mourinho's side. He also stressed a dip in the central defender's form convinced him to make the "important decision" for the team.
Conte is unhappy with the recent reports suggesting his relationship with Luiz has deteriorated. The Italian manager expressed his disappointment that he is being questioned over the defender's fitness.
"I understand that someone is thinking that I'm not telling the truth. I'm disappointed about this, but I can understand it," Conte said in his pre-match press conference before Southampton clash, as relayed by Sky Sports.
"I like to tell you the truth at every moment. I'd like to tell you a bad truth rather than a good lie. I will try to solve the situation. I think we can call the doctor and organise a (media) conference with the doctor for him to explain the medical situation."
Any move by Arsenal for Luiz in January will see them face competitions from last season's Champions League finalists. The Daily Mail reports Juventus and Real Madrid are also interested in the player.
The Old Lady are believed to be ahead of the Spanish capital club in signing the 30-year-old. Juventus and Real can provide tough competition for Arsenal in securing Luiz's signature if he decides to leave Chelsea.
In Luiz's absence, Andreas Christensen has impressed for Chelsea. Luiz is likely to find a tough task in displacing the Danish defender from the starting lineup, especially after the latter's impressive display in recent times.