It seems to be capped somewhere below 200 units for a single mission, though I can't find a recent, definitive source.
The requested cargo quantities do seem tied (loosely) to the trade rank of the mission / pilot, i.e. higher rank tends to produce higher quantity requests, but amounts vary substantially depending on the mission.
There don't seem to be any authoritative listings of specific missions scenarios, e.g. actual cargo amounts and required ranks. The best I could do was crawl screenshots until I found a forum post from 2015 that includes some actual screenshots from in-game.
Keep in mind this information is dated, but it shows several different ranked missions, from Peddler to Elite. The quantity of the cargo does not seem tied directly to the rank of the mission (Merchant has a few higher quantity missions than the Elites), but the higher ranks do seem to have the biggest quantities.
The highest listed in this forum post is 138 units for a Merchant-rank mission, but Cmdr Freiheit has added in comments that he has seen upwards of 160 units for an Elite mission. These are the highest quantities I can find out-of-game, and my rank is only Broker at the moment, so I am unable to test in-game.