At Rome & China there are a number of writings by various Chinese authors reporting on the relations between these two countries. They describe the geography between Syria and China; the culture and habits of the various peoples; the cities and their rulers; and the engineering in in these cities. Accounts are given for the period 166 A.D. to 1333 A.D.
Ta-ts'n or Li-kan is Roman Syria. In 166 A.D., An-tun (Marcus Aurelius Antoninus) is said to have sent an embassy to China. "From that time dates the direct intercourse with this country". In another report for the same year, Ts'in-lun, a (Roman) merchant of Li-kan, (presumably on an embassy and perhaps the same one) reached Cochin-China where its prefect sent him to the court of the Chinese Emperor, Sun-ch'uan, who aked him to draw up a report on the Roman Empire.
In 643 A.D., Constans II Pogonatus is reported to have sent an embassy to China.
The Chinese report that at Fu-lin (Byzantium), "They have clever physicians, who by opening the brain and extracting worms, can cure mu-sheng (a sort of blindness)", i.e., trepanny. There is a clepsydra(?) with twelve golden balls which fall to the side of a golden man and tell the hour accurately.
Crossing the desert south of Constantinople (sic), one comes to the two countries of Kush where the black natives are most violent. Illicit 'intercourse' is practiced on these natives to show who is master.
One out of every seven days they (Romans) refrain from business and carouse all night.
In 1333 A.D., Pope John XXII is said to have aappointed a replacement archbishop to Peking. Presumably, a Christian community existed there and/or the archbishop was a Papal ambassador.
A sea voyage from India(?) to Li-kan is said to be three years long. Is a voyage around Africa contemplated?
In all, it was a difficult read for me, as the Chinese names did nothing but confuse me. But the lists of animals (a sheep whose belly is attached to the earth), building materials, and trade goods was fascinating.
A 'Buddda", said to be Christ, was reported.
Except for the sentence quoted in the second paragraph above, there seems to be no other direct statements as to relations between the two states. Nonetheless, it appears that these two nations were in direct contact with each other.