The countries have not yet made a formal announcement, but four sources have revealed details of the sales to Reuters.
Any drone shipments to Ethiopia risk aggravating already-strained relations between Ankara and Cairo, which is at odds with Addis Ababa over a hydropower dam on the Blue Nile.
Two Egyptian security sources said Cairo had asked the US and some European nations to help freeze any deal.
A third Egyptian source said any agreement would have to be raised and clarified in talks between Cairo and Ankara as they try to repair ties.
One Turkish official said Ethiopia and Morocco had both requested purchases of Bayraktar TB2 drones in agreements that could also include spare-part guarantees and training.
A diplomat said separately that Morocco had received the first batch of armed drones it ordered in May. Ethiopia plans to acquire them but the status of that order is less clear, the envoy said.
It is not known how many drones were involved in the deals, or financial details.
Ukraine and Turkey's Nato partner Poland have also ordered armed drones, which military experts say are cheaper than those made in Israel, China and the US.
Official data show Turkey's defence and aviation exports rose sharply to Morocco and Ethiopia in the past two months but details of drone sales are not provided.
Growing interest in armed drones is a boost for the Turkish government at it tries to increase exports to help ease its economic problems, and underlines the growing importance of armed drones in modern warfare.
Defence and aviation exports to Ethiopia rose to $51 million in the first three months of this year, from $203,000 in the year-earlier period, with a jump in August and September, according to the Turkish Exporters Assembly.
Exports to Morocco totalled $78.6 million in the same period, with $62 million in September alone.