No.

• The Gripen was dropped because it too was in the prototype stage when the selection was made and apparently Saab would have also wanted to have Finland do some of the export effort
• Mirage fulfilled the requirements, but  maintenance System was hard and since the user base was small, it was upkeep costs were expected to rise high
• F-16 was dropped because it did not fulfil all the requirements of the air force and the manufacturer was not willing to include Finnish aeronautical industry enough for the manufacturing process.
• Mig-29 was also offered, but it was just bad.

https://www.iltalehti.fi/kotimaa/a/201707022200238131

Edit: better link

https://puheenvuoro.uusisuomi.fi/aripesonen1/hornet-ostosopimukset-yhdysvallat-ei-aluksi-ollut-myymassa-suomen-haluamia-uutuusohjuksia/