The 47-year-old Uruguayan has made no secret of the fact he is desperate to further strengthen his squad next month with goals a priority, but he knows too how difficult the winter market can be.
Sporting director Lee Congerton is the man charged with the task of fulfilling Poyet's wishes, and the latter knows he will have to remain patient.
He said with a smile: "Yes, we want the best player in the world very cheap, nice-looking, he can score goals, he can run, sprint.
"But it's difficult, very difficult
We are working, I can tell you we are working very hard
Are we going to bring in someone? Are we going to buy him, loan him? We will see, it depends on so many things.
"Certain kinds of players are only available on loan; certain kinds of players, you need to buy them and it costs a lot; certain players, they cost less because they are a nightmare or they have got some issues and you think you are the genius who can bring them to you and calm them down.
"If you see what happens in Spain and Italy - Fernando Torres goes one way and then Chelsea go maybe the other way, and that starts making things happen.
"We are working very hard, very hard
It's not easy, but we will see."
Poyet's main focus is not difficult to identify with his team having scored only 16 goals in their first 19 Barclays Premier League games of the season, and the fact that forwards Steven Fletcher, Connor Wickham and Jozy Altidore have contributed just six between them is an added concern.
But asked about the chances of boosting his strike force, he replied: "The easiest way to sort out a few problems in front of goal is to go and buy.
"Now the right price, the right player who scores goals coming here and doing it straight away - everybody is looking for the same, so it's a competition
There are not many, but we will try."
If he faces an anxious wait on the transfer front, Poyet has at least received better news on injuries with three players due to return to training.
Sebastian Larsson, who damaged an ankle in Sunday's 0-0 draw at Aston Villa, is expected to train on Wednesday and could yet be available for Thursday's trip to Manchester City, although fellow midfielder Liam Bridcutt will play no part at the Etihad Stadium.
Poyet said: "Seb Larsson is going to train tomorrow
He feels much better
The injury is the kind of injury we can all react to differently
It's going to be painful for a while because he twisted his ankle badly, but the damage to the ligament is not that big.
"It looks bad because it's swollen, so it depends how you cope with the pain
From what I have seen, Seb is quite confident that he is going to train tomorrow
He knows it's going to hurt, but he is willing to go ahead, so he is looking good.
"Liam Bridcutt, protocol, we are going to go with the rules
There are certain rules - he looks perfect today and is desperate to get out and desperate to play because he loves the chance to play.
"But we have been talking a lot about these concussions and we are going to go with the rules, so until, I think it's Friday, he cannot even train, so we are going to keep him safe."
Meanwhile, full-backs Patrick van Aanholt and Anthony Reveillere are expected to resume training next Monday after recovering from a dislocated shoulder and a calf problem respectively with the Dutchman a week ahead of schedule.
Source : PA
Source: PA