Poyet is keen to have an answer soon as to whether Italy striker Borini - his main transfer target - will join the club.
The Italian is said to have turned down a permanent move to Wearside, but Poyet has not given up on his man just yet.
"I think we're getting close to a final decision either way because it's been a bit too long," the Black Cats boss told Sky Sports.
"It's time now that it's a yes coming or a no, as we need to move on."
United were denied their first competitive win under Louis van Gaal on Sunday as Jack Rodwell's equaliser secured a 1-1 draw for the hosts in the Premier League clash at the Stadium of Light.
Juan Mata put United ahead in the 17th minute, providing a close-range finish to Antonio Valencia's cross.
But Rodwell broke his Black Cats duck 13 minutes later by heading in a Sebastian Larsson corner to draw things level.
The result means the Red Devils have got their first point of the new league season on the board.
But just over a week on from their campaign-opening home defeat to Swansea, Van Gaal's men again looked unconvincing, even with Robin van Persie back in the team.
"It was a good game to watch," said Poyet.
"We played a very good first half, going forward taking chances and creating half opportunities after conceding at what was the wrong time really because we were in control of the game. It was a big effort.
"We made a few decisions on how to play against a different system and the boys have done exceptionally well. We showed that we were organised and difficult to play against."
In his post-match press conference, Poyet had some sympathy for Ashley Young, who was booked for diving, and was relieved not to have conceded a spot-kick.
He said: "It was tough on Ashley. The only problem with Ashley is his reputation. Before he even went for that ball, everybody was expecting him to jump, but that reputation is unfortunate.
"I didn't think it was a yellow card. I am not sure if it was a penalty. It was one of those that is even difficult for the referee. Either way, some people will be upset, some people will be happy.
"It was one of those. It was a difficult 50-50 and the outcome was only because of what has happened in the past and it's not fair on him. I don't like it."
Poyet was understandably pleased with his side's performance on an afternoon when summer signing Will Buckley shone in his first start for the club.
The Uruguayan said: "I am so pleased that he had a very good first half because now everybody knows why I was so consistent in asking the club to bring him.
"It took us seven and a half months - we got him here and now everybody knows why, because he is electric, because he's direct, because he brings the stands into a different feeling, the atmosphere.
"He is going to do plenty of things. Now, don't expect it every week - £2.5million. People pay £30million and £40million and £50 million - we paid £2.5million, so let's be patient.
"But he showed why he is here and that makes me very happy."
Meanwhile, Poyet refused to comment on reports that former Chelsea frontman Salomon Kalou is a target during the remaining days of the transfer window.