The Uruguayan has seen his side take just one point from their last four Premier League matches as the prospect of relegation looms large at the Stadium of Light.
Several Sunderland players are out of contract at the end of the campaign but Poyet confirmed that his mind is on winning games and not discussing new terms.
"I have not told any of the players who are out of contract that they are free to look for another club this summer," he was quoted as saying by The Sunderland Echo.
"I think the players are clear enough. No one has come to me and asked me about it.
"I didn't want to start talks anyway because it can be taken the wrong way if you are not careful.
"My view is that players have to take the attitude of when does my contract finish? 30th of June?
"OK, then I'm a player for this club until the 30th of June."
And ahead of the trip to Liverpool on Wednesday, Poyet stressed that contractual situations would not be a factor in his team selections for the remaining 10 games of the campaign.
"I'm the head coach here, I will play you regardless of your contract situation - and I want you to give me everything, regardless of your contract," the 46-year-old added.
"That should be enough. Your contract does not finish in January, it finishes in June.
"So give me everything until June and if you show me everything in training, I will play you anyway, regardless of your contract situation.
"It doesn't matter if we offer a player a contract and he says he's not going to sign - that doesn't mean I'm not going to play that player anymore.
"He will play, I promise you, if he's impressing me with his attitude and his ability in training.
"But I think that that approach of having respect and trust for each other is working so far, so I've got no problems with any of the players in that direction."
