The Blues centre-back trained away from the rest of Frank Lampard’s squad on Wednesday.
He is one of a number of central defenders on Unai Emery’s shortlist ahead of the transfer deadline, but Sky Sports News understands there has been no formal bid for the Brazilian yet from the Gunners.
Chelsea are reluctant to let him leave for the Emirates Stadium given their current transfer ban, as they would not be able to sign a replacement this summer.
Luiz is under contract at Stamford Bridge until 2021 after signing an extension in May of this year.
The 32-year-old made 36 Premier League appearances and scored three goals last season, his most ever during an English top-flight campaign.
Unai Emery is in the market for further defensive options and Arsenal are expected to make a final push to sign Celtic left-back Kieran Tierney before the deadline.
Meanwhile, Laurent Koscielny has departed north London to join Bordeaux.