Black Cats boss Poyet remains hopeful Borini will complete a season-long loan deal ahead of Monday night's transfer deadline.
Borini spent last term on Wearside on loan, and had been expected to complete a hassle-free return to the Stadium of Light in the new campaign.
The 23-year-old's potential move has stalled across the summer, though, with Poyet claiming he cannot reveal all the reasons.
"I know how people feel but unfortunately we cannot give you all the information, all the true information on why he's not with us," the Uruguayan said.
"I know from the outside it looks like it's him not wanting to come to Sunderland because of whatever, but I can promise you it's not like that.
"Now I keep it open because he's still a Liverpool player, and maybe he can still become a Sunderland player.
"Yes, I still want him
I know Fabio
I am a believer that when you know the player and you know what you get, and you are convinced that is the right player with the right mentality, I'll wait whatever is needed for a player like that.
"I think (Liverpool boss) Brendan (Rodgers) was clear now that it's up to him, but the situation is better for us, I hope
We'll see."
Sunderland slipped up 1-0 at QPR on Saturday, leaving Poyet's men still without a Barclays Premier League victory in the new season.
Poyet remains upbeat about the prospect of a "special" transfer before the transfer window closes, but admitted trying to pull off several coups under the radar.
"I said the other day every time we talk about names or there are rumours other teams get involved and it doesn't help, so we're trying to do things as quietly as possible and get them over the line," he said.
"We're going to do something: we have to because of the numbers.
"We're trying to do something special, but that will depend what happens in the next two days.
"I don't want any panic buys."
Gritty midfielder Lee Cattermole was fortunate to escape a red card at Loftus Road on Saturday, sniping at Leroy Fer just moments after being booked.
Poyet said he remains unfazed by Cattermole's temper, and is pleased to see some passion from his uncompromising star.
"If I was worried about his character I would change things," Poyet said.
"I had a word with him at half-time and everything was all right.
"If we were all very nice it would be boring for you - you couldn't write about anyone.
"He knows that sometimes when we are not doing well he's the one that shows a little more frustration than the rest
But that's his character
"I like to have that kind of character
I don't like all very nice
It's my thing - I need a little bit of nastiness.
"He's not my Luis Suarez - he's my Dennis Wise!"
Source : PA
Source: PA