The 24-year-old recently called up British radio station BBC Radio One and was asked if it's true that she's the baby's godmother.
She said to radio host Greg James: 'Oh, you know. I don't want to reveal anything to you guys. That's really up to Elton and David [Furnish].'
She added: 'I'm too much of a lady!'
John and Furnish welcomed baby Zachary on Christmas Day, when he was born via a surrogate, and Gaga admitted she has met the little boy.
She said: 'I've actually met Zachary and he's the most beautiful boy and he's so loved by Elton and David and they love him so much. It's really a beautiful family.'
The star was speaking just minutes before the world premiere of the video to her new single Born This Way and said she wasn't dressed and her hair wasn't done.
She said: 'I just woke up, my hair looks very funny and I have a big, giant cup of coffee in my hand.'
Asked what she was wearing, she said: 'I'm actually just wearing... is this okay for radio? I'm wearing just some black underwear and a bra.'
The star also revealed she is a big fan of British artist Adele.
She said: 'I love Adele, I think Adele is so wonderful.'