Poyet's men face a stiff task to claim a result at Anfield on Wednesday, with Liverpool seeking a seventh successive Premier League victory to move within one point of leaders Chelsea.
Brendan Rodgers' side have scored 24 goals during their current winning streak and will be high on confidence after thrashing Cardiff City 6-3.
The 20-year-old Wickham was recalled from a loan spell at Leeds United on Monday and will be rushed straight into Sunderland's squad.
Sunderland will be without Fabio Borini – ineligible under the terms of his loan from Liverpool – while Steven Fletcher is battling an ankle injury.
Wickham has made just nine league starts since arriving at Sunderland in 2011, but Poyet has revealed he may feature from the beginning on Merseyside.
"We've been trying different things, different situations," Poyet said on Tuesday.
"Fabio is not available, so I'm going to keep trying different things.
"Connor is an option. I can't keep closing my eyes, keep picking the team until the end of the season and think why didn't I try that.
"It's my job to keep searching for the solution and then you know you've done everything."
Poyet believes a lack of expectation could work in Sunderland's favour at Anfield.
"We need to be a very good team because they (Liverpool) have been scoring for fun," he added.
"We need to change that goalscoring situation somehow. At different times during the game, they're going to be pressing, especially with the excitement around Liverpool Football Club right now.
"No-one expects us to do anything. But we've got a chance to go there, relax, play our football and defend well."
Sunderland sit 18th in the Premier League table, three points adrift of safety, although they do have up to three matches in hand on their relegation rivals.
