Costel Pantilimon, Billy Jones and Jordi Gomez moved to the Stadium of Light on free transfers at the start of the summer but, since then, Poyet has failed to bolster his squad.
The Sunderland boss is thought to be pursuing last season’s loanees Marcos Alonso and Santiago Vergini, as well as Cristian Rodriguez from Atletico Madrid, and he hopes to make signings quickly as the Black Cats prepare to head to Portugal for a pre-season tour.
Poyet told the Sunderland Echo: ““I’m waiting and waiting, which is not nice.
“You’re expecting to do a couple of deals, but they’re not happening.
“People say don’t be anxious or nervous. I think there will be at least one in by tomorrow and I hope at the weekend we can have three in.
“But the word I’m saying is ‘hope’. It’s a matter of time, but, as the days go past, that becomes difficult.
“We are waiting, we are desperate to do something in the next few days because we are going to Portugal and we need to have as many players as possible in place by the time we get there.”
Liverpool accepted the Black Cats’ £14million offer for Fabio Borini last week and Poyet has not given up on landing the striker, who is with the Reds on their US tour and appears to be inclined to remain at Anfield.
He added: “I think we need to be honest. The more time that goes past, it looks to me like we have less chance.
“Some people think the opposite. The more players Liverpool sign, then there is more chance. Let’s see who is right and wrong.
“We’ve got specific targets and it’s taking a little bit too long. We have time for one or two specific players, but the rest, we don’t have time.
“We don’t have a left-back. We need a left-back now. We need pace, which we have been looking for for the last year.
“We need a couple of midfielders too after we lost Craig Gardner, Jack Colback and Ki. There are things we need to do. It will be a real shame if we go through this week and those players are not right.”
But Poyet confirmed Marseille winger Morgan Amalfitano, who spent last season at West Brom, is not among his possible targets.
He said: “Right now, I will say there is not a real interest in Amalfitano.
“I followed him when he was at Lorient before he went to Marseille, so I know the player from four years ago.
“It was nice to see him in England playing last season. But in that position, we’re looking for a second striker – which will hopefully be Fabio Borini – and pace, whereas Morgan has more ability on the ball.”