The pop veteran was enjoying a family getaway when Grande, who happened to be a fellow guest, took part in a talent contest at sea.
"I think she sang the song from 'Titanic', which may have been a very tough choice on a cruise ship, but she blew my mind to the point where I went looking for her parents and got ahold of her mom," Gloria tells Access Daily.
"I told her, 'Listen, I don't know what Ariana wants to do with her life and what you have in the works, but your daughter is a star... and her voice is mind-blowingly spectacular.' "
"Then, years later... she's being everything she can be - an amazing singer and growing and evolving and doing all new things. I'm very happy and proud for her."
Grande has also shared similar story years ago. When appearing on British show "Alan Carr: Chatty Man", the "7 Rings" hitmaker spilled, "I was on vacation with my family and I was doing karaoke and it was a terrible song choice. We were on a cruise and I decided to sing 'My Heart Will Go On' from 'Titanic'. Really dark choice, but I was only six or seven so I didn't know what I was doing."
"After I was done somebody came up to me and was like, 'Gloria Estefan would like to speak to you,' " she went on recalling. "I was like, 'Are you serious?' and my brother was like, 'Are you f*****g serious?' And we went together to go say hi to her. She was like, 'I just want to let you know that you are so talented and do not ever give up.' It was crazy."