There are two different stories this could be referring two, both from Chinese sources (The Chinese, by and large, had more information on Rome than the reverse. This is possibly because they were more involved in the politics of the Steppe, or simply because our evidence from China is much closer to the court). One is the military expedition of the general Ban Chao, which either reached the far western end of modern Xinjiang, or all the way to the Caspian Sea, depending on what you are reading. He sent one Gan Ying out as an envoy to Rome (called Daqin), who reached the mouth of the Persian Gulf before turning back. The traditional account is that the duplicitous Parthians deceived him to prevent his meeting with the Romans, which I don't believe for two main reasons. One is political: this occurred in 97 CE, a year before the accession of Trajan. While Trajan would carry on a war against the Parthians, before him there was a succesful and comfortable policy of detente going back to Nero. Secondly is geographic: according to Chinese sources, Gan Yin was told that a round trip journey to Daqin could take anywhere from three months to two years, which strikes me as entirely reasonable. Sailing in the Indian Ocean went in a cycle based on seasons, and if you missed your mark you would need to wait out until the monsoon wind turns in your favor again. So Gan Ying turned back, along with a report on Roman customs that swings between fanciful and accurate.

The second instance was the meeting of two "ambassadors" of the emperor "An Dun" (Probably Antoninus Pius or Marcus Aurelius) of Daqin in 166 CE. These were a few people picked up in one of the southern commanderies, who bore gifts for the emperor as tributes and tokens of friendship. The Chinese records say with some disappointment that the goods were all things from southeast Asia like wood, spices and animal products, which points to them probably not being ambassadors but actually some quick thinking merchants who came up with the story when picked up by Han soldiers.

There was also a Roman merchant named Maes Titianus who went exploring and probably reached as far as Tajikistan before turning back, although the whole affair is rather poorly documented.