Among the tracks on "To Nancy, With Love" are songs performed by Bono, Morrissey, Jon Spencer, Pulp's Jarvis Cocker and Richard Hawley.
The Morrissey collaboration, "Let Me Kiss You," is being tipped for early release as a U.K. single, the magazine reported.
"A few of my songs have made it through the years," said Sinatra, whose hits include "These Boots Are Made for Walkin'," "Some Velvet Morning" and "Somethin' Stupid."
"Most of the rest bit the dust," Sinatra said. "Except with Morrissey. He seems to know and love them all. And this song is very much a Nancy/Morrissey song. It's gorgeous and beautiful and romantic and lovely."