/u/shlin28 has a special interest in this topic, and has answered a similar question here. If you went through his posting history, you would find numerous other posts on Rome and China. In that link /u/buy_a_pork_bun also discusses the Chinese perception of the Romans.The tl;dr of these posts is that we don't have any evidence specifically pertaining to what attitudes these two powers held towards each other, but there is certainly evidence of contact between Eastern Rome and China. Aside from a few Greek Christian sources, the Chinese source "The Book of Tang" appears to be a crucial primary source on this matter. I should emphasise that the posts I have linked above refer more to the late form of the Roman Empire we tend to call the Byzantine Empire and their relationship with China, especially between the years 500-700 AD. Hopefully /u/shlin28 or an equally informed poster can come and elaborate, or expand on the nature of Rome's relationship with China in the classical period.