Poyet only took over at the Stadium of Light last month, succeeding Paolo Di Canio following Sunderland's dismal start to the season.
The Uruguayan's arrival has prompted an upturn in form, with the club winning three out of five matches in all competitions - including a derby success against Newcastle United - and climbing off the foot of the Premier League table.
However, Poyet has made it clear he wishes to be in control of who is brought in during the January transfer window - rather than director of football Roberto De Fanti, who oversaw a raft of arrivals during Di Canio's tenure.
As published by The Guardian, Poyet said: "We talked about a position the other day and considered four players.
"I picked two. One of the other two (selected by De Fanti) was a definite no.
"If that one is coming, I won't be here. The player has to be the right one for me. If not, I'm not going to accept it.
"My situation is clear. I met with Roberto and Valentino (Angeloni, the chief scout) and said what I think I need. They need to give me the options and I need to pick the ones I like."
"I'm sure it's going to be done in the right way, in the common-sense way. Everyone has a responsibility and then the player has to be the right one for me."
Poyet insisted he has no problem working alongside either De Fanti or Angeloni.
"So far, everything is working fine. The connection and communication have been great," he added.
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