There have been great Islamic scholars throughout the Islamic world, including regions which were part of the Persian Empire and the Roman Empire.
Scholars who are from regions that were once part of the Roman Empire include scholars from Al-Andalus, North Africa, parts of the Arabian Peninsula, and some other parts of today's Arabic-speaking world. (I'm sure you can find some examples from each region if you look!)
That said, the centre of the Roman Empire (Rome) and the regions immediately surrounding it (such as most of Italy and Greece) never became part of the Arab-Muslim Empire. Usually the capital or centre of a civilisation has the greatest scholarly output and resources. (That is apart from the conquest of Byzantium. and that happened rather late in Islamic history.) In contrast, the heart of the Persian Empire was absorbed into the Arab-Muslim Empire. So this could be a factor.
It could also be a matter of nomenclature. The regions of the Roman Empire that were integrated into the Arab-Muslim Empire were usually more on the fringes or outskirts of the Empire, and generally the people there did not identify themselves as "Romans"; they were simply under Roman control. For instance, Islamic scholars from Egypt would not have identified themselves as "Roman" despite the fact that Egypt was once a Roman province. In contrast, many people from the Persian Empire were identified as "Persian".
So, perhaps these may be factors.
In any case, there have been Islamic scholars from all these regions.