Both clubs have already agreed the fee for Borini but Poyet's efforts to convince the player to move to the Stadium of Light have so far met with frustration.
However, the Uruguayan has reiterated his desire to seal the club record transfer and believes it could even be completed before the season starts at the weekend.
The 23-year-old Italian spent last season on loan with the Black Cats, scoring 10 goals in 40 appearances, and played a key role in the club's run to the Capital One Cup final.
Poyet told Sky Sports News: "The idea was to have the deal done a few weeks ago, 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."
Poyet has been busy this summer adding Jack Rodwell, Billy Jones, Jordi Gomez, Costel Pantilimon and Patrick van Aanholt to his squad.