The Liverpool striker spent last season on loan at the Stadium of Light, scoring 10 goals in 40 appearances in all competitions, and was a key figure in guiding the Black Cats to safety.
Poyet had earmarked the Italian as one of his main targets this summer, but despite having a £14 million offer accepted by the Anfield outfit, a deal with the player himself has so far proved elusive.
But the Uruguayan now believes there is genuine cause for optimism in their pursuit of the forward, and said he expects movement on the deal in the next few days.
“The idea was to have the deal done a few weeks ago,” admitted Poyet to Sky Sports News.
“But for different reasons it was impossible, but we are confident that maybe in the next few days we can do something about Fabio.
"I'm always thinking that we can add quality players, especially the ones we know, and let's hope that confidence I am trying to bring to the club is confirmed...with the signing of Borini."
Sunderland have already displayed their willingness to splash the cash this summer, having secured the services of Manchester City midfielder Jack Rodwell for £10 million.