Carroll could return to the starting lineup for the Hammers following a spell on the sidelines through injury, and he will be looking to continue the good start that he has made to his time at Upton Park.
Wenger insists that he never doubted the 23-year-old's quality, but hinted that his £35m move to Liverpool may have come too early.
"Carroll has the quality and that will come out with time. We expect Carroll to be at his best - it is down to us to deal with that. We can only focus on our own performance and be at our best," said Wenger.
"He started very well, then he had to deal with a high level of expectation with a massive transfer on his shoulders going to an historic club where a lot was expected of him. Maybe it was a bit too early for him.
"Since I have seen him at West Ham, he looks back to the Carroll we have seen at Newcastle, that means with less pressure."
Carroll averaged one goal every 5.2 games during his time with Liverpool, compared to one every 2.75 games with Newcastle United.