We can't prove a negative, but there's no reason to believe Justinian had any such plans.
For one thing, it's unlikely Justinian would've felt the need for a co-star. The usual rationale given for dividing the empire is that Roman territories were too vast for a single person to rule effectively from one centre. And indeed, Justinian might have ran into the same trouble if the Byzantine reconquest had proceeded more successfully.
However, Justinian did not send Belisarius west in 535 "to reconquer the former Western Empire"; rather, he sent Belisarius north from Africa to recover just Italy from the Ostrogoths. There is, obviously, a significant difference between ruling Italy from Constantinople, and ruling Italy + France + Britain + Spain from Constantinople.
In 535, re-imposing imperial rule on Italy was not obviously unduly onerous for a sole emperor.
It should also be stressed that the invasion of Italy was an opportunistic move, exploiting the internal instability of the Ostrogothic Kingdom at the time. Likewise, the campaign for North Africa was initiated only after the Vandals engaged in a power struggle. So even if Justinian had given thought to achieving his grand ambition, he could not have expected it to happen any time soon.
As a matter of fact, when Belisarius reclaimed North Africa for the Eastern Empire, Justinian organised it as a praetorian prefecture answering to Constantinople. It's much more plausible to expect that he was planning on doing the same if the reconquest of Italy succeeded - and that was exactly what he ended up doing.
Moreover, note that despite Diocletian's institution of the Tetrarchy, the Roman Empire continued to have sole emperors from time to time. For example, Constantine I and Theodosius I. In other words, it wasn't necessarily impossible for one man to rule the Roman Empire - it just takes a powerful leader which wasn't always available.
Justinian the Great was a powerful emperor.
Note also that, unlike many of his predecessors, Justinian did not personally lead troops into combat but chose instead to act through appointed generals. An emperor campaigning in Iraq could easily find it impossible to deal with developments in Gaul if barbarians chose to invade. or usurpers decided to rebel. An emperor residing in his capital, however, will have a much easier time remaining in control.