Former Charlton and West Ham manager Curbishley has already intimated he would be interested in replacing McCarthy, who was sacked on Monday, if he receives the call from Morgan. But Press Association Sport understands former Sunderland boss Steve Bruce would also be interested, while ex-QPR manager Neil Warnock has also been linked with the role.
Morgan, who returns from a skiing holiday on Wednesday, said: "Now that Mick is no longer with the club, we will be having conversations with people in the coming days. We have to see who's available and who is the right fit for the club, somebody whose personality suits Wolverhampton Wanderers."
He added: "We don't know whether it's somebody who will run things until the end of the season or whether it's going to be a permanent position. But we can't afford to hang around. We need to take some action in the next few days."
When asked about Curbishley, Morgan told Sky Sports News: "He's got a great track record, he's been there and done it before, and he's exactly the calibre of person that we're looking for."
Morgan admits he was not content with Wolves battling against relegation and decided to end McCarthy's reign after five-and-a-half years at the helm.
He said: "Wolves has historically been one of the great clubs in English football. Hanging around the bottom few places and relegation is not what this club is about.
"We need to pick ourselves up and be aiming up the league and hopefully that's what the new man will take us forward with. We have ambitions and fighting relegation is not one of those ambitions."
Wolves chief executive Jez Moxey concedes the accent will be on candidates with Premier League experience, and he said: "This job is not a job for a novice. You keep an open mind but winning matches in the Premier League is the most difficult part of this whole scenario.
"We have to have someone in we think will win games in the Premier League. It's not like we have been cut adrift at the bottom. We're in there with four other clubs and we've got just over a third of a season to go."
Source: PA
Source: PA