The ancient Roman Empire and the ancient Chinese Empire were both extremely powerful and were pervasive in their respective regions of the world. You don't often hear them discussed in the same context, but it turns out they did know about each other. Or at least the Chinese were aware of the Roman Empire.
"Daqin" was the ancient Chinese word for the Roman Empire or the part of it that they knew existed, which is where modern day Syrica is today. The ancient Chinese were probably aware of the Romans because of their place at the end of the famous trading route, the Silk Road. The Chinese maintained one end of the route and knew that Daqin was on the other end.
While the ancient Chinese never actually made contact with the Roman Empire, Genearl Ban Chao did send an envoy, Gan Ying, to travel to Daqin in 97 AD. He never made it though because he stopped when he reached a coast and was told it would be dangerous and take a long time to cross it. Gan Ying wrote extensively about the Roman Emperor but most of his knowledge was likely from secondhand information.