The Italian impressed on a season-long loan in the North East last season and played a prominent role in helping the club retain its top-flight status.
Reports on Saturday had suggested that the Black Cats had agreed a £14m fee with Liverpool for the 23-year-old's services, and Poyet now confirms that the deal is all but sealed.
"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 struck 10 times in all competitions for Sunderland last term.