Justinian was a Roman
Latin was his native tongue. He thought of himself as a Roman. His Empire was still, to all purposes, very identifiably Roman.
And his goal was quite naturally a restoration of the Roman Empire - renovatio imperii. If Alexander provided anything, it was the same thing for any number of previous Augusti - a martial inspiration, not a political forebear.
And as others have noted, the opportunity for expansion was there in the splintered and unstable Germanic West, not the vibrant and powerful Sassanid East. And the residue of Roman (and Chalcedonian Christian) culture still surviving in these old provinces of the Western Empire would make for areas which would be much easier to retain and govern than anything Justinian would find in Mesopotamia or Persia.
At most Justinian would - if the opportunity presented itself - look for minor or tactical advantage in the East, with minor acquisitions in Armenia, the Caucusus, or northern Mesopotamia, and exaction of tribute. But I can't see him desiring - or gaining - more than that under any circumstances. His ambitions lay in the West.