Unai Emery has admitted to holding talks with Shkodran Mustafi about a potential move away from the club.
The Germany international remains the most expensive defender in the club's history but has received criticism from some quarters ever since joining from Valencia in 2016.
The 27-year-old was jeered by a minority of fans as he came off the bench during the Emirates Cup defeat to Lyon and has been linked with a transfer for most of the summer.
Emery worked alongside Luiz for a spell while in charge at Paris St Germain but played down any suggestion that the Brazil international could be one of his five allotted captains at the Emirates Stadium.
"It's difficult," he said when asked if Luiz would be considered.
"I think we have the possibility inside with players with more circumstances to achieve my decision for a captain.
"But he has experience to use not with the armband but he can still help the young players with his experience. Not like one of the five captains, but doing that."