SAAB has demonstrated the ability to integrate Erieye on multiple platforms with remarkable ease & at relatively low cost. It was developed on a Fairchild Metroliner, IIRC (because the Swedish air force could lend one to SAAB), made operational on SAAB 340, then Embraer 145, Saab 2000, & now, in the upgraded Erieye ER model, on the Bombardier Global 6000.The GlobalEye that exist today is probably too small to meet all NATO needs (modified Bombardier 6000 business jet). Of course Saab can offer their system integrated on a larger airframe, however it will take some time to do that integration & testing, and it will increase cost. Also big NATO countries that already picked the E-7 (US, UK, Turkey) will probably push hard for E-7. Tiny Sweden has not even been accepted as NATO member yet , so I think this will be a hard sell for Saab.
The Bombardier 6000 is a pretty big bizjet (max TO 45,000 kg - E-7's 77,000 or so). Different league from the turboprops Erieye has been fitted to. And given SAAB's performance to date I expect that fitting it to, e.g., an A320neo could be done rather easily.