Borini scored 10 goals in 40 appearances on loan at Sunderland last season and played a key role in the club's run to the Capital One Cup final.
"We're working on it," Poyet told Sky Sports News. "It's not easy, it's been a difficult summer, I think, for everybody.
"We are not finished. We need more bodies. We are looking for specific, quality players."
When asked if there is a timescale to conclude the Borini deal, Poyet said: "If you asked me last week, I probably would have said this week, but I cannot tell you next week because we will wait for him.
"Of course, we need to do other business that is important for the team. I have a shape. You don't realise it, but we are 10 days away [from the start of the season]."
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