Funny enough, there was some limited contact between the two. The Chinese referred to the Romans as Daqin, 'Great Qin', itself suggesting that the Chinese saw the Romans as a great dynasty like the Qin before the Han. Fuckin' Parthians put effort into making sure the two didn't meet though - would've been bad for Parthian trade if the Parthians weren't in such a great position as middlemen, with two major business partners almost completely unaware of each other. Good business sense though, I'll give the Parthians that.