"As a punk rocker from New York, I've basically been hoping that I would become so good that one day I would piss off Madonna," she said.
Lady Gaga told Attitude magazine she was not intentionally competing with Madonna in the disco arena and didn't know quite what to think about Madonna's rendition of the Gaga smash "Born This Way" during a recent concert in Israel.
"That's just not what I'm about," Gaga said. "She chooses to use her voice the way she chooses to use hers and I choose to use mine the way I use mine."
The Los Angeles Times said the 27-ear-old Gaga wasn't so nonchalant last month when she zinged Madonna in a Twitter tweet to her Little Monsters stating Madonna was a fading star who hated her.
"I don't need anybody's permission to be remembered," she wrote. "I will be."
2014: The Year in Music [PHOTOS]