Sources have confirmed to Us weekly.
Qualley, 22, was previously linked to "The Fault in Our Stars" actor Nat Wolff after they were spotted hanging out together last summer, while Fukunaga, 39, fuelled romance rumours with Michelle Williams in the past.
On the work front, Fukunaga, whose credits include "Beasts of No Nation" and "True Detective", has been busy working on TNT's upcoming thriller series "The Alienist".
Meanwhile, Qualley will appear on May 21 episode of "The Leftovers", which airs on HBO.
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