The Black Cats appeared to receive a double set-back in their pursuit of the pair earlier this week when Borini's agent Marco de Marchi indicated that the player's preference was to fight for his place at Liverpool, while a report from Italy suggested Fiorentina full-back Alonso was no longer for sale.
However, Poyet remains optimistic that deals can still be struck for the two men who provided sterling service during loan spells at the Stadium of Light last season.
Asked about 23-year-old Borini, the Uruguayan 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."
The capture of 23-year-old Alonso too is a priority, and one which Poyet is confident can be achieved.
He said: "It's close, but not close enough. Everything is on track.
"We're trying hard. It's been a bit more difficult than I expected, but we're not going to stop."
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