I've never heard of such texts, but you've got me quite interested. Do you have anything more to go on?

From about 1371 to 1567, private overseas trade wasn't so big. I say this assuming the texts you have in mind would be primarily for private traders, not government translators who would have official offices to handle that sort of thing. This was during the hǎijn 海禁 period, a two-centuries-long ban on private sea trade. Official tribute missions were still permitted and frequent for a time, but for private traders, the state made an effort to prevent independent commerce.

However the tribute missions were a fairly large deal. Foreign trade was in part handled by the Sìyíguǎn 四夷馆, which served the purpose of imperial translators. It was through the Sìyíguǎn that official documents were translated, both outgoing documents meant for trade partners, as well as incoming messages meant for the court. Within the Sìyíguǎn, internal departments were set up for different languages. For example, a Thai department was started in the latter half of the 16th century as trade increased.

Likewise in Joseon, on the Korean peninsula, there was a similar department, called the sa yeog won 司譯院, the "department of translators", which has a coincidentally similar sounding name to the Ming version. People were learning languages, and there are things like the Nogeoldae 老乞大 ("Old Cathay"), an important Ming-through-Qing textbook for learning Mandarin for Koreans, but I haven't heard of trader phrasebooks. I can't speak for other major powers, but I would imagine the situation was much the same as far as official translation offices.

But again, for things like phrasebooks means for traders, I can't think of anything from around the Ming that this would refer to. In the late 19th and early 20th century, these did exist, and we still have things like Chinese pidgin English phrasebooks means to help English speakers communicate with traders in ports like Guangzhou and Shanghai, but the linguistic politics of the period were quite different, and it wasn't something the Qing was putting out there.

So if you can give me anything more to go on, I'll be happily to see what I can dig up. Like I said I'm quite interested. If these things are out there and really from the Ming, they would be an incredibly important linguistic resource.