The note in the NET lists no one is declared righteous before him as an Old Testament allusion rather than a quotation.

David, speaking to God in prayer, wrote what was translated into Greek in the Septuagint as ἐνώπιόν σου (before you [NET], in Your sight [NKJV]).  Paul, writing about God, wrote ενωπιον αυτου (before him [NET], in His sight [NKJV]).  Apparently it is the verb that is negated in Greek rather than the subject: not justified or not declared righteous are all living or all flesh.  David wrote πᾶς ζῶν (all living, translated no one alive [NET], no one living [NKJV]).  Paul changed it to πασα σαρξ (all flesh, translated no one [NET], no flesh [NKJV]).  The change is interesting considering what Paul had to say about the flesh (sarx, σάρξ) later in Romans 7 and 8.  But Paul himself used σαρξ (flesh) and ανθρωπος (man, human) interchangeably in Galatians 2:16.  First, ου δικαιουται ανθρωπος εξ εργων νομου (no one is justified by the works of the law),¹ then, εξ εργων νομου ου δικαιωθησεται πασα σαρξ (by the works of the law no one will be justified).²