According to Reuters, the decision will be announced at the NATO summit in Ankara, Turkey, on July 7-8.
Both NATO and Saab have declined to comment to Reuters.
Saab rose sharply on the Stockholm Stock Exchange on Thursday and closed up 8.6 percent.
Today, NATO has 14 AWACS planes that have been in use since 1982. They are based at Geilenkirchen Air Base in Germany and have been extensively used for NATO's various surveillance missions over the years.
Global Eye competes with American Boeing's E-7 Wedgetail, which is based on the 737 passenger aircraft.
US scrapped plans
Last year, NATO abandoned previous plans to buy six Wedgetails after its largest customer - the US Defense Department, the Pentagon - scrapped plans to buy 26 such planes in favor of relying more on satellites.
However, under pressure from Congress, Defense Secretary Pete Hegseth told a congressional committee in May that the Pentagon was pushing to reinstate the aircraft in the budget.
At the end of May, news broke that Canada had begun negotiations to purchase Global Eye, which is a surveillance and management system.
The negotiations will include determining how many planes will be delivered. However, Micael Johansson, Saab's CEO, said at the time that it would be around six planes.
It also means that Canada has rejected competing bids from the United States.
Global Eye is based on the Canadian aircraft manufacturer Bombardier's Global 6500 model.
Additional plan
A year ago, Saab also signed a letter of intent with the French Defence Procurement Agency (DGE) regarding the sale of two Global Eye aircraft to France.
That deal also includes an option to purchase two additional planes.
The United Arab Emirates has been using the system for some time.
The Swedish Armed Forces also use Global Eye, of which one of three ordered planes has already been delivered to the Air Force.
Saab's Gripen fighter jet is also included as one of the possible options in another potential deal with Canada, which wants to replace its older American planes.
