Other aircraft under consideration are Boeing's F-18 Super Hornet, the Eurofighter Typhoon and the F-35 Joint Strike Fighter from Lockheed Martin.
"We note a great interest for Gripen worldwide and we follow the decision that has just been announced in Denmark," said Lennart Sindahl, the head of Saab's Aeronautics business area. "Now we are looking forward to receiving more information about the process.
The Danish Ministry of Defense had suspended its competition for a next-generation fighter in 2010.
The Gripen is a lightweight, single-engine, multi-role fighter with a delta wing and canard configuration. It has a maximum speed of 1,372 miles per hour at altitude, a combat radius of 432 nautical miles and a service ceiling of 50,000 feet.
The government of Sweden ordered 60 Gripens last month. Saab said Switzerland is a potential customer for 22 of the aircraft.
Notable deaths of 2014 [PHOTOS]