The Molineux outfit parted company with Mick McCarthy on Monday, with a 5-1 home defeat to West Brom at the weekend the last straw.
With Wolves looking to avoid Premier League relegation, Morgan has admitted that Curbishley in on the side’s shortlist of potential new bosses.
“He’s got a great track record,” Morgan told Sky Sports.
“He’s been there and done that before. He’s exactly the calibre of person we’d be looking for. There are a number of other candidates as well. I don’t really want to be drawn into a conversation about who we’d be talking to just yet.
“Clearly we’d be interested in someone of his calibre.
“We’ll have to see who’s available and the right fit for the club, somebody’s personality who suits Wolverhampton Wanderers.
“It’s very, very early to say yet, but we won’t be hanging around. We need to take some action in the coming days.
“This has all happened very, very fast. We have spoken about potential candidates, but we’ve not spoken to anybody.
“We wouldn’t speak to anyone while Mick was in place and quite rightly so.
“Now that Mick is no longer with the club we will be having a number of conversations with a number of people in the coming days,” he admitted.
Wolves are currently in 18th place in the table with 13 games remaining.
By Gareth McKnight