He said his character "looked at humanity ... and was a real cynic."
"He'd seen a lot of tough stuff as a doctor. I think he worked in war-torn areas and stuff," Gyllenhaal said of his character, adding that he "maybe hoped that space would be as we all hope, the new frontier."
"It was interesting to play a character like that, because I feel the same way sometimes about things that are going on down here," he said. "But I think being here and staying here, particularly in this country, you know, now and in the world, is the most important thing."
Gyllenhaal added that he would not go into outer space even if he could, saying, "I'd like my feet on the ground, you know."
The actor said that he did enjoy simulating being in zero gravity while he filmed the movie.
"They put you in a harness, and then you're flying around," he said. "It's a strange thing for your brain to get around, but it's also really fun."
Strahan joked that Reynolds had a "man crush" on Gyllenhaal.
"Well, I think he has fantastic taste, that's for sure," Gyllenhaal said in response. He added that the two are great friends and that when he was on set with Reynolds, "I literally — I could not stop laughing. "I mean, he's just hilarious. And I just love his family, and ... he's just a good dude."
In addition to working in films, Gyllenhaal is currently starring in a Broadway revival of "Sunday in the Park With George," a musical about the painter Georges Seurat.
"It's the closest thing to my heart of almost anything I've ever done, I have to say," Gyllenhaal said of the show.
Gyllenhaal said that the two were able to get tickets to see his play through the children's hospital and that they said "it gave them a respite from everything that they were going through. And it gave them inspiration, and it reconnected them in a really hard time."
"That's why I do what I do," he said. "To me, that connection is a deep inspiration."
Gyllenhaal's latest film, "Life," is currently in theaters nationwide.