Both players made big contributions last season, aiding Sunderland in their last gasp escape from relegation and journey to the Capital One Cup final.
No fewer than 12 players have left the Stadium of Light since the Premier League season drew to a close two months ago, leaving Poyet with a threadbare squad in serious need of strengthening.
Borini and Alonso have been the Uruguayan's top two transfer targets this summer, and although deals are yet to be completed for either, the Sunderland manager remains confident.
A £14 million agreement has been reached with Liverpool, but the Wearside club are yet to commence personal talks with the 23-year-old, leaving large pockets of the media to speculate that the Italian will snub a move back to the Stadium of Light.
Poyet however seems fairly relaxed regarding the progress in the deal, speaking in a press conference yesterday the 46-year-old said; “I can assure you though that there is no disappointment on my part that it has not happened yet,”
“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.”
The Black Cats appeared to have been dealt a blow yesterday concerning their pursuit of Marcos Alonso.
However, again, Poyet remains hopeful that a deal can be reached for the left-back. Speaking about the Alonso deal the Sunderland manager said; "It’s close, but not close enough, Everything is on track."
“It’s just like I explained before. These deals for everything to come together, so many people need to be happy. It’s not that easy."
The Sunderland manager has spoken of his desire to have 20 of his 23-man Premier League squad in place by the time the Black Cats fly to Portugal for their pre-season, and with that set to kick off on the 29th of July, some serious progress will need to be made over the next few days.