The 65-year-old singer has previously collaborated with stars including Ed Sheeran, Shania Twain, Nelly Furtado, Jennifer Lopez and Mary J. Blige but he admitted that he wants to record with Taylor because his 12-year-old daughter Virginia is a Swiftie.
Virginia told The Mirror newspaper: "I love Taylor Swift and am going to one of her concerts in a few days. It would be amazing if he worked with her next".
Andrea added: "I've thought about it and it could be a great thing".
Virginia - whose mother is Veronica Berti - has followed in her father's footsteps by becoming a singer but he doesn't want to put any pressure on her.
He said: "When she sings it makes me very happy. Children have to be free, and I hope that when she is older, she does what her heart tells her".
And Virginia added: "It's pretty much normal [singing with my dad]... I usually do at least one or two songs and have got used to it now".
Meanwhile, Virginia recently reflected on their first official performance together, four years ago.
She told 'Loose Women': "I think the first time was when I was 8-years-old in Palma. I wasn't supposed to sing. I'm not sure how it happened".
Andrea explained: "I had to sing 'Hallelujah' and it has a lot of English words so I asked Virginia to learn the song to sing it with me".
The pair also enjoy singing 'Bambina Mia' together, as it holds a special meaning for them.
Virginia said: "The song is about a dad who is talking to his daughter about life and love. I got emotional when I was recording it, it took a long time to record it because I was bawling then my dad noticed and made fun of me".