The 34-year-old attended a meeting with senior figures at the club on Friday which concluded without an extension to his existing agreement.
Sources say the Gunners have made clear their respect for Luiz's contribution but are seeking to strengthen the centre-back area with younger alternatives.
It is unclear whether Luiz was offered any terms to stay but regardless the Brazil international is now focused on finding a new club, sources said.
He has claimed on several occasions that he wants to finish his career back at Benfica, adding in April last year: "In football everything changes -- what is true today, tomorrow is a lie -- but my feeling is not.
"I love Benfica. My dream is to step on the pitch of Estadio da Light in their colours. Benfica is bigger than any player."
Luiz joined the Gunners from London rivals Chelsea in 2019 for £8 million. He has made 73 appearances for the club to date -- including helping them win last season's FA Cup Final against his former club -- and has been viewed by manager Mikel Arteta as an influential leadership figure in the dressing room.
He is suffering with a hamstring problem but will hope for one final appearance in Arsenal's remaining two Premier League matches, against Crystal Palace and Brighton next week.