By coincidence I actually emailed Binance this morning about the availability of buying Nano OTC, they replied:

"Hi mortuusmare,

Thanks for finding us!

OTC trades are done on your existing binance.com account, we require that your account passes the regular KYC process for trading on the exchange (i.e. Level 2 verification). Trades are usually done on chat (Telegram or WhatsApp), and we move coins directly into and out of your binance account. Trade records are found on the "Distribution History" on the website.

We don’t currently trade fiat. No fees on trades. Our price is the price we trade at and it's a "negotiation". Yes we quote Nano!

The minimum trade size is usually 20 BTC and we generally need coins in your account before we trade.

If you are interested we can open a chat room. Please let us know your handle and we will reach out to you on chat. Or you can join our Binance OTC telegram group here: https://t.me/joinchat/J-QnERBI2Z5VQHdJTC3Q-g

Thanks! Binance OTC"