The Italian's agent has this week played down the prospect of returning to Wearside.
Asked about 23-year-old Borini, Poyet told the Sunderland Echo: "It is not for me to explain but it is not just a question of Fabio wanting to come or not. There are many, many things to look at and unfortunately, I cannot comment on those.
"We are involved in negotiations and you never know how long that can take. There's nothing new to report as things stand, but we are still hoping to close the deal completely.
"It's up to Fabio. We have been clear, everything is fine, there's no doubt about his connection with our club, and me and him get along fine, so there is no reason for it not to happen.
"I would love to know how long it will take to sort out, but all I can tell you is that things are changing every day.
"We have targets that we are looking for, we have other options, but we have an agreement with Liverpool and we will do everything possible to get Fabio to the club first.
"If Fabio does not come, it does not set us back, we would move on - we are not a one-player team."
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