Wickham spent time on loan at Sheffield Wednesday and Leeds last season before returning to play a big part in the Black Cats' escape from relegation.
The 21-year-old striker scored five times in three games in April as Sunderland collected seven crucial points against Manchester City, Chelsea and Cardiff.
Now he has a year to run on his current deal and the club need to extend his stay or cash in quickly to avoid a repeat of Jack Colback's free transfer to Newcastle this summer.
"For me, Connor's situation is clear, he needs to sign a new contract or we let him go - we sell him," Poyet told the Sunderland Echo and the Journal.
"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."
Source : PA
Source: PA