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 at 3:50 p.m. the share was up 8.1 percent.
Today, NATO has 14 AWACS aircraft 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.
GlobalEye competes with Boeing's American 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 headquarters, the Pentagon - scrapped plans to buy 26 such aircraft 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 GlobalEye, which is a surveillance and management system.
The negotiations will include determining how many aircraft will be delivered. However, Micael Johansson, Saab's CEO, said at the time that it would be around six aircraft.
It also means that Canada has rejected competing bids from the United States.
GlobalEye 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 Defense Procurement Agency (DGE) regarding the sale of two GlobalEye aircraft to France.
That deal also includes an option to purchase two additional aircraft.
The United Arab Emirates has been using the system for some time.
The Swedish Defense Forces also use GlobalEye, of which one of three ordered aircraft 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 aircraft.
