GaGa was said to be pleased to meet 'School's Out' rocker Cooper because he influenced her stage shows, but he revealed that he warned her against letting her stunts and on-stage persona become part of her everyday life.
Cooper - born Vincent Furnier - told Reader's Digest: "She said, 'Alice, thank you for letting me steal your show.'
"I said, 'GaGa, I created a character called Alice. But it's important to keep Alice on stage. I never let Alice take over my real life'.
"I guess what I was trying to say was, 'Be outrageous for the cameras. Wear a chicken on your head. But don't get suckered into thinking that stuff is real. When you're at home, just be yourself. If you can learn to co-exist with both GaGas, you'll be okay'."
Cooper's wild behaviour nearly got too much and he struggled with alcohol problems earlier in his career, but managed to replace his addictions with golf.
"If you take alcohol away from an alcoholic, that addict will try and get hooked on something else," he continued. "For me, it was golf - and when I say hooked, I really mean that. The first time I hit a ball, I knew I'd found my new drug.
"Of course, the great thing about golf is that it actually makes you healthier - I turned 64 this year and I've never felt better. I guess it's all about peace.
"For so many years, my life has been filled with the chaos of rock 'n' roll, but when I walk onto the course, it's just me and the ball: a moment of stillness."
Watch Alice Cooper performing 'Poison' on Strictly Come Dancing below: