The Canberra-based technology company announced on 3 March that it had received a purchase order of $7 million for the advance purchase of long-lead items.
The products will be deliverable from 2017-2020.
The companies are expecting to reach final agreement within 14 days.
EOS specialises in technology for weapon systems optimisation and integration as well as intelligence, surveillance and reconnaissance for land warfare.
EOS said its key products are next-generation armoured vehicle turrets and remote weapon systems.
Orbital ATK is an American company specialising in aerospace and defence technologies. Orbital designs, builds and delivers space, defence and aviation systems for customers around the world as a prime contractor and merchant supplier.
Orbital said its main products include launch vehicles and related propulsion systems; missile products, subsystems and associated space components and services; and advanced aerospace structures.
The business is headquartered in Dulles, Virginia and employs 12,000 people in 18 states across the US and in several international locations.