Director Jon Turteltaub says there are no firm plans for National Treasure 3 which is understandable because of Disney's success with other franchises:

“My prediction and my fear is you will see 'National Treasure 3' on [Disney's] streaming platform.” 

“I feel it deserves the big movie treatment, and I'll make a [ton] more money if it's a movie, so [I don't like] streaming.” 

On the cast returning: 

“We'll probably all say 'yes' because we love it and each other so much. But you got to hit everybody on the right week.”

 More: 

“How do you not make another movie when the movies leading up to it are all internet memes?”