They had seriously reliability problems regarding the Russian engines, I recall. Russia already pulled out, but I guess they can either get back in business with the Ukrainians or develop their own (possible together with India). Ukraine can't bring it to market alone, because of the lack of good engines, without Russia they have to turn to the West for engines which seriously limits its export potential... putting it in direct competition with C-130J and A400M.
NATO has already An-124s on lease, the aircraft and pilots provided by one of those UK/Ukrainian commercial companies. Actually, production was started again. Furthermore some NATO countries are ordering C-17 transports to create a transport pool for them. Actually the coordination of these and other NATO/EU transport capabilities is stationed near me at Eindhoven AB in the Netherlands at the European Airlift Centre...which has now merged with the Sealift Coordination Centre into the Movement Co-ordination Centre Europe´ (MCCE).
As you can see the shortage really lies in the strategic/heavylift capability, not really the An-70's class. That's why you see the UN chartering An-124s and Il-76s and not L-100s (commercial C-130s)...