The showbiz patriarch has several tracks that the 'Back to Black' singer - who died at the age of just 27 in July 2011 - recorded with National Youth Jazz Orchestra but he isn't sure if they will ever get an official release.
He told BANG Showbiz: ''I've got a little bit of stuff that Amy recorded with the National Youth Jazz Orchestra, but really there isn't a lot, but there is some stuff. I don't know if it will come out. But her musical legacy will look after itself whatever happens.''
In the wake of Amy's passing, a posthumous compilation album, 'Lioness: Hidden Treasures', was compiled by her producers Mark Ronson and Salaam Remi and Amy's family and featured unreleased songs, demos and cover versions.
Mitch admits he is still finding it hard to come to terms with his daughter's untimely death and he is only just starting to realise what an important artist she was.
He said: ''I was so busy running after Amy and telling her off and doing dad things that I didn't realise how good she was until now, I've really started to listen to the music and listen to the words and listening to her singing and I realise how brilliant she was. And I have to say, and I know I'm her dad, but I don't really think that a lot of people can compare to Amy.
''Tony Bennett says Ella Fitzgerald, Dinah Washington, Amy, Aretha Franklin in no particular order are the best. He regards her as one of the top female singers of all-time. She was such a normal kid and her music came from her heart, you listen to her songs, and some of them are very painful for me to listen to, but when she wrote a song it was like she was cutting her arm off. She was never going to be prolific she was never going to write a thousand songs, Irving Berlin got up and wrote a song everyday, she couldn't do that.''