The 23-year-old made an impact while on loan at the Stadium of Light last season and the Black Cats boss is optimistic that he can persuade him to leave the Reds permanently
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With personal terms still to be discussed with the striker, Poyet is hopeful that he can persuade the Italian to return to the Black Cats.
"We've agreed terms with Liverpool and we are waiting for the documents to be signed and then we'll move on from there," he told Sky Sports News.
"Like any other deal you do, first you need to sort out the clubs and then you start working with the player.
"I'm hoping we can have him because he knows how much it would mean for us to have a player like Fabio."
Borini started for Liverpool in a 2-1 friendly win over Preston on Saturday.