"Cat school is something that you could do as much of or as little of as you wanted. I was in cat school a lot," Swift told Today host Hoda Kotb.
"You're crawling around on the floor, you're learning about their anatomy, their impulses, their instincts, how they sense things," the singer continued.
"I still can't believe it," Hayward said about appearing alongside an all-star cast. "I just tried not to like dwell on it too much and just try and treat everyone like they're just normal people."
Cats, from director Tom Hooper, is set to hit theaters on Friday. The film is an adaptation of Andrew Lloyd Webber's Broadway musical of the same name, which is based on author T.S. Eliot's book Old Possum's Book of Practical Cats.
Kotb also asked Swift about recently being honored with Billboard's Woman of the Decade Award and the speech she gave, which touched on her career, sexism in the music industry, struggles she has endured due to being a woman and how Scooter Braun has acquired her music catalog from her former label Big Machine Records.
"If it's going to help someone else and it's something that I see as truly beneficial to other people, I think it's important to express yourself and in music you know, as women we need to have each other's backs," Swift said.