There appeared to be little chance of the 21-year-old earning fresh terms at the Stadium of Light at the end of March, with loan spells having been taken in at Sheffield Wednesday and Leeds United.
Wickham was, however, recalled to Wearside to aid a survival bid and contributed five crucial goals as Sunderland preserved their Premier League status.
He is now considered to be an important figure, with the potential which saw him complete an £8million move in 2011 finally being fulfilled.
Wickham is, however, only tied to a deal until next summer and Poyet is wary of allowing that agreement to run down and risk losing a saleable asset on a free transfer.
He said in the Sunderland Echo: “For me, Connor’s situation is clear. He needs to sign a new contract or we let him go – we sell him. There is nothing in between.
“He is an asset to the football club and we paid a lot of money for him.
“Last year, he was a key part of us staying up and he was very important. But he needs to realise that the club needs to look after the interests of the football club as well.
“I suppose that, one way or another, we are going to have an agreement.
“Which one of those is going to happen, I don’t know – it is not my job, that is (sporting director) Lee Congerton’s department.”
While conceding that his hand may be forced, Poyet remains confident that the Wickham situation will be resolved.
He added: “Last year I was the happiest one because I talked to him before he went to Sheffield Wednesday and I talked to him when he came back.
“I spoke to him when he came back from Leeds and I told him that every single player wants a run of four or five games.
“I told him that you won’t get that situation many times, but he had it with us and he responded.
“Now the situation has changed a little bit. But I am not worried it.”