The 21-year-old played an integral role in keeping the club in the Premier League last season, scoring five goals in three games in April as Sunderland pulled off a great escape.
Wickham, who had loans spells with Championship sides Sheffield Wednesday and Leeds United in the 2013-14 campaign, has just a year left on his contract and is yet to agree a fresh deal.
Sunderland head coach Poyet has warned the former Ipswich Town man that he will be sold if no agreement is reached.
The Uruguayan told the Sunderland Echo and The Journal: "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 the other, we are going to have an agreement.
"Which one of those [two outcomes] is going to happen, I don't know -- it is not my job. That is (sporting director) Lee Congerton's department."
