The versatile Brazilian is out of favour at Stamford Bridge, and it looks more then likely that Jose Mourinho will look to cash in on the former Benfica man.
With Mourinho desperate to land a top class striker this summer, the Portuguese will have to offload some of his players to fund the deal, in accordance with financial fair play.
Whilst Luiz would not come cheap, his strength, speed and versatility could prove crucial for Arsene Wenger's side.
Luiz has proven his worth in the holding midfield role - a position Arsenal are known to want to strengthen.
With Mikel Arteta and Mathieu Flamini currently the only defensive midfielders in the Gunners' squad and lacking in both pace and power, Luiz's athleticism could prove an interesting foil.
Luiz - also capable of filling in at right-back and his more natural centre-back - would also solve act as cover for several defensive positions.
With Bacary Sagna looking likely to leave the Emirates, Luiz would be a fourth choice centre-half should they require him there, and also offer an option at full-back.
Even if Luiz were to cost Arsenal in excess of £20million - as he surely would - the North London club would save in the sense that they would only have to buy one player to cover three positions.
The move would also suit Luiz.
Additional game time would be a huge selling point, as would the opportunity to play in a more attacking side.
Being able to still live in London would also attract Luiz, who wouldn't require any time to settle into the league.
Last summer Arsenal regretfully failed in a bid for a certain Luis - and Wenger should make sure he doesn't similarly regret missing out on Luiz.
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