Bennett made the prediction after recording a collaboration with the 'Judas' star for his upcoming Duets II album.
"I never met a more talented person in my life... I think she's going to become as big as Elvis Presley," he told Billboard.
The pair have recorded a rendition of Babes In Arms musical classic 'The Lady Is A Tramp' for the album, which will be released on September 20.
Bennett also revealed that he tried to help late singer Amy Winehouse with her addiction to drugs when he recorded a duet with her earlier this year.
"I was convinced I would be able to help her and talk her out of... taking drugs," he said.
His duet with Winehouse on 'Body and Soul' will be released as the second single from the album, with the profits to be donated to the foundation set up by Winehouse's parents following her death last month.
Bennett said that releasing the duet to generate the proceeds is "a great way to turn something positive out of this".
The performer recently compared Winehouse to some of the greatest jazz singers of the past.
> Lady GaGa sings 'Happy Birthday' to Tony Bennett - video
Watch the music video for Lady GaGa's new single 'You and I' below: