The 51-year-old pop icon was impressed by the 'Paparazzi' singer – who is a self-confessed Madonna fan – from the first time she saw her, even though she was still refining her act.
Madonna told Rolling Stone magazine: 'When I saw her, she didn't have a lot of money for her production. She had holes in her fishnets, and there were mistakes everywhere. It was kind of a mess, but I can see that she has that 'IT Factor'. It's nice to see that at a raw stage.'
Lady Gaga has cited the 'Celebration' singer as an influence on her career and Madonna insists she can see similarities between them both.
She added: 'I see myself in Lady Gaga.'
Lady Gaga recently revealed she was thrilled when Madonna attended one of her concerts in New York.
The pop star – real name Stefani Germanotta – said: 'My sister texted me and she was like, 'Madonna is 15 feet away from me. And there are two guys having sex in the audience. I just remember thinking, 'Wow, this is exactly what I wanted. I've got Madonna and I've got gay sex!' "