TONY BENNETT teamed up with LADY GAGA to sing "The Lady Is a Tramp" for his last album, "Duets 2" (which you can hear below).  And now, they're joining forces for a bigger project.

Tony tells "Rolling Stone", "She called me and said, 'I want to do a jazz album with you.'  And I said, 'You got it!'  So that's one of the things we're gonna do.  [It's going to be] a big swinging album."

The album will feature songs by a "mystery songwriter," who Tony wouldn't name so nobody steals their idea.  He does say he hopes to hit the studio with Gaga, quote, "as soon as I can."

Tony is apparently a HUGE fan of Gaga's.  He says, "A lot of people don't know it, but she's a phenomenal jazz singer.  She's a good friend and I respect that she's so creative . . . I call her the musical Picasso.  Her energy is just phenomenal."