The Newcastle United goalkeeper was hurt in a collision with Manchester United's Marcus Rashford in last weekend’s 4-1 defeat at St James's Park.
Darlow, 30, played on after the incident midway through the second half.
“He’s still sore,” said United head coach Steve Bruce. “But he’s made a huge improvement from where he was on Saturday night. We’re going to have to take it down to the wire. It’s an impact injury, there’s no tear, but it’s in a very sore region where he’s taken an awful knock.
"He’s better than he was, but whether he’s going to be fit or not, we’ll have to see over the next 48 hours. He’s waited patiently for his chance, then was thrown into it with the freakish injury of Martin (Dubravka).
Summer signing Mark Gillespie is on standby to play if Darlow can’t recover in time to play at Molineux.
Bruce said: "Mark has played in the cup competitions, and done well, but we hope he (Darlow) can make it.
“It’s why we brought him (Gillespie) here. He’s played there times in the cup, and that looks a good shout now, especially if he has to make his debut. He’s an experienced goalkeeper who has played in the Scottish Premiership for four or five years.”
Newcastle-born Gillespie, 26, joined as a free agent after his contract at Motherwell expired.