Poyet confirmed last month that terms had been agreed with Liverpool to bring Borini back to the Stadium of Light after a successful loan spell in 2013-14.
But the Italian's move to Sunderland was put on ice following a shoulder injury sustained during Liverpool's pre-season fixture against Roma in the United States.
Sunderland remain interested in Borini and speaking after Thursday's 2-0 win over Real Betis, Poyet said the club were staying patient in their pursuit of the 23-year-old.
"We're still waiting," said Poyet.
"There's no more than last week, no more than next week. We're waiting but it's still ongoing. I'm still confident it will happen."
Borini netted seven goals in 32 league appearances as Sunderland avoided relegation last season.
The former Chelsea youth product also scored three goals in the Capital One Cup, including the opener in the decider against Manchester City.
"I don't think the word is 'frustrating' because we knew after he travelled and the [shoulder] injury that it would take a bit longer," added Poyet.
"We'll keep working because we know him very well.
"Fabio ticks all the boxes because we know what we're going to get and how important it is for us and the fans as well. We are in a very good position... waiting.
"It's that last step, that little thing that is going to close it. Sometimes it's easy, sometimes it takes a bit longer."