The 57-year-old singer would love to see the 21-year-old star take to the stage to play her in the production because she has been a big fan of the raven-haired beauty's ever since she saw her doing karaoke on a cruise ship when the 'Problem' hitmaker was just eight years old.
She explained: ''Ariana Grande would be somebody wonderful.
''I saw her when she was eight years old on a cruise ship and she had sung this song, and I literally went up to her and told her and her mom, 'I don't know if you plan on doing this, but this is what you need to be doing because you are an amazing singer.' ''
Gloria insists the star's karaoke performance was ''amazing'', especially as she was yet to reach double figures in age.
Speaking to the New York Daily News, she added: ''She was doing karaoke and we were listening because I love to go watch that stuff and it was amazing!''
Musical 'On Your Feet', named after Gloria's 1989 hit 'Get One Your Feet', is set to hit Broadway in the summer of 2015.
The play will tell the story of Gloria and her musician husband Emilio Estefan - who she married in 1978 - and their rise to becoming worldwide sensations.
Several hit songs are set to feature in the musical including 'Rhythm Is Gonna Get You', 'Conga', '1-2-3' and 'Live For Loving You'.
Earlier this month, auditions for the production were held in Miami and New York but the cast is yet to be announced.