Wolves have revealed one person was offered the manager's job before
On Friday the club denied the search for Mick McCarthy's successor had become an embarrassment, amid reports several candidates didn't want the job.
Chief executive Jez Moxey, speaking on BBC1's Final Score, said he wanted to set the record straight.
"To suggest we've thrown the managerial job around like confetti just is not true," he said.
"One manager was offered it and one manager and us could not come to a conclusion.
"Terry Connor was the next man offered it and he accepted the job."
Moxey did not reveal the identity of the first candidate to be offered the role. Steve Bruce, Alan Curbishley and Neil Warnock were interviewed, while Reading boss Brian McDermott and Brighton manager Gus Poyet were all linked with the role.
Former Everton and Rangers manager while Connor has been promoted from assistant manager until the end of the season.
The chief executive had initially said he wanted an experienced Premier League manager, but, speaking on Friday, he backed Connor's credentials.
"I would refute he is a novice totally because Terry Connor has been central to our successes with Mick McCarthy as a team," he told BBC Radio 5 live.
Asked if the process had been an embarrassment, Moxey said: "We would refute that. I think we have carried out a very diligent process of interviewing. Those discussions remain private and confidential."
Wolves, who are 18th in the Premier League, sacked McCarthy on 13 February - the day after a 5-1 home defeat by Black Country rivals West Brom.
Connor, 49, has been given the role until the end of the season, which means he will be in charge for 13 Premier League games, starting with a trip to Newcastle on Saturday.
"We are satisfied with the process we have followed and we have seen a variety of candidates and given ourselves the best opportunity to assess the current market of managers. We have done that properly," said Moxey.
"We said to our fans we would appoint a manager prior to the Newcastle United game and we have done exactly that.
"We think he is ready. It frustrates me that all we concentrate on is the chairman, manager and perhaps the captain.
"You forget there is a huge business beneath those principal people and we concentrate very much on ensuring our structure is strong."
Connor, who has served under four managers in 13 years at Wolves, said he was proud to step up.
"I've told the players to take things one game at a time. Let's get through Saturday [against Newcastle] then look to move on to Fulham.," he said.
"It's a privilege and honour to look after the team until end of season. We feel there's unfinished business. I'll still be known as TC. I have to earn 'gaffer'.
"The challenge I've got is to keep the side up with 13 games remaining. My job is to get the players ready for each game. I've known Mick for a number of years. We couldn't be more different in our approach to certain things. Mick has his own way and I've got mine."