The Canadian stars met at the 2017 Billboard Music Awards where Drake, 32, told Celine, 51, that he was "'like a year away from a Céline tat" on his body.
Speaking at the time, Drake said: "It means the world, you're very iconic. We love you. I'm like a year away from a Celine tat."
However, now Celine has issued a public plea to Drake not to get the personal inking.
In a video for iHeartRadio Canada, Celine said: "Please Drake, I love you very much. Can I tell you something? Don't do that.
"You can write me love letters, you can send me autographs for my kids, you can come and visit. I can have you home for lunch or dinner... we can go for a drink. We can sing together. Whatever you want to do - I can talk to your mother - whatever you want! But please..."
Celine added she didn't want Drake to get her face etched on his body as due to aging, the tattoo will eventually wrinkle and her face will look "not pretty".
She added: "Please don't tattoo. If you do it, just do a fake one so you can change your mind."
Meanwhile, Celine recently shared that her new album 'Courage' will be "very fun" and "very different" to her other work and feels she's "opened her wings" on the new record.
She said: "The album sounds very fun, very different and I did try new things. It's still me but I have opened my wings to embrace new writers and producers.
"Just to be open to different sounds. I'm not doing like an AC DC heavy metal, but there's different flavours."
The 'My Heart Will Go On' hitmaker kicked off the 'Courage World Tour' this month, and recently admitted she would have a "breakdown" if she looked at her all the dates.
Celine - who has son René-Charles, 18, and eight-year-old twins Nelson and Eddy with her late husband René Angélil- confessed that the global run "would not happen" if she acknowledged how long it would take as she fears she'd miss her children too much.
She said: "When I go on a tour you cannot look at all the dates because you'll have a breakdown and the tour will not happen. My heart won't go on. "