"That absolutely made my day when I read that because I'm a huge fan of hers," Swift tells CMT Insider in an interview airing Saturday at 1:30 ET.
Gaga, 24, who said in an interview that she starts singing along to Swift's song "so loudly" when she hears it on the radio that she's "so embarrassed," had also praised the country star, 20, for being "a great songwriter."
"It's a great song!" Gaga told Show Studio. "I think it's just because it's very whimsical in a way that I'm not necessarily whimsical every day."
And Swift returns the feelings: "I'm a huge fan of hers and [hearing] that really, really made me smile," she says. "I appreciated that."
Although they are in completely different genres, Swift says she admires Gaga for her daring style and music. "I remember the first time I ever saw [Lady Gaga] on [MTV's] TRL," recalls Swift. "She had like a leotard on and I just thought to myself, that's so daring. Her music must be daring like that and [I] went home and I downloaded 'Just Dance.' "