The Uruguayan has made it clear he wishes to add to his ranks when the window reopens in the new year, with Sunderland having registered just three Premier League wins in the first half of the season.
However, Poyet is realistic in his assessment of the club's dealings, and knows the acquisition of the right targets can take time.
"Yes, we want the best player in the world very cheap, nice-looking, he can score goals, he can run, sprint," he quipped.
"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."
With just 16 goals in 19 league games, Sunderland are the third-lowest scoring team in the division, but Poyet knows bringing in a proven goalscorer is not simple.
"The easiest way to sort out a few problems in front of goal is to go and buy," he said.
"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."
