In various sources that deal with the history of Indian state Kerala, it is stated that they had trade contacts with ancient Egypt, as well as with ancient Greece and ancient Rome, these contacts were through maritime routes. They were direct routes as well as through arab traders. Here is one source about Keralan history
http://www.prokerala.com/kerala/history/history.htm#h2
Among buddhist writers there are some who think that Rome had also intellectual contact with India, like Alex Wayman for example.


I have heard that Roman coins were found in Vietnam some years ago.