The Brazilian center back left the Gunners after a relatively successful stint in the summer, as they secured the signature of Brighton's Ben White.
According to Globo.com, Flamengo are ready to make Luiz a formal contract offer after working out the financial details of their proposal.
The club's vice president Marcos Braz and manager Giuliano Bertolucci are working on the best way to assess the situation surrounding the 35-year-old.
They wanted to see if any European team came in for Luiz.
Now that the European transfer window is closed, they may see an opportunity to secure him on an affordable deal.
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