The Han Dynasty was aware of a great Empire in the distant West, and the Romans were buying Asian silk via the Persians. The Persians were the intermediaries for the two empires on trade. Unlike modern times, the trade routes were national secrets, not shared publicly to insure Perisan monopoly on trade access. Ironicly in the late Han Dynasty there was a great land exploration expedition composed of 100,000 men who traveled westward till they reached the Caspian Sea. The leader decided to go north and ran into cold vast steppes and he returned to China concluding that there was nothing of value. If he had gone south he would have reached the eastern outposts of the Roman Empire. History would have been different
The Chinese court also sent a delegation to the Roman Empire, by sea; alas it arrived in the Persian Gulf and never made direct contact. The ambassador praised the ethical nature of the inhabitants of Mesopotamia.