Poyet saw his side concede four goals in his first game in charge against Swansea last weekend, meaning they have leaked 20 goals in their eight Premier League games to date.
Former Manchester United defender Brown has not played a first-team match since January 2012 due to a series of injuries, but he came through 90 minutes for the Under 21s last week and is back training with the squad.
Poyet admits Brown could be the answer to his side's defensive frailties, but knows it could be a risk throwing him back into the starting XI so early.
"Wes is fit and he's been training with us all week and he played in a behind closed doors friendly we had on Tuesday," said Poyet. "It's a decision we need to make.
"Whether somebody's fit enough to play 90 minutes or not, or how many players there are in that situation you can't take a chance. But you can't have too many on the pitch that can't play 90 minutes. Depending on that, we will make a decision on it.
"He could be everything that you need in the Premier League.
"He's experienced, he's played at the highest level, at one of the best teams in the world, and he knows the game well. Hopefully we can see him very soon on the pitch."