Wilder's time in charge of his boyhood club ended on March 13 when the 53-year-old left Bramall Lane by mutual consent following a disastrous season, with the Blades having propped up the Premier League table all season and destined for a return to the Championship.
Speaking to Sky Sports News, Prince Abdullah explained the time-table to the exit of Wilder, who had significant issues with the club's hierarchy regarding a number of issues, including recruitment. The Blades supremo also gave his opinion on criticism of the Blades' transfer policy.
He said: "In December, Stephen (Bettis, Sheffield United CEO) told me that Chris had talked about resigning. I was really worried and I knew that a phone call or a Zoom call would not do the trick, I had to sit with him.
"The problem was, because of Covid, all Saudis were banned from leaving the country. I spent two weeks trying to get permission to leave. As soon as I got that, I flew to London and drove to Sheffield and met Chris before the Southampton game.
"I told Chris, if we lose every game until the end of the season, we are not going to fire you. We need you to be our coach. I am not talking about emotion, I just believe you are the best manager to bring us back to the Premier League.
"I told him recruitment could be better and that we could sit down after the season and talk about how we could make it better.
"I told him that I am not happy that sometimes after defeats when you talk to the media (and say), 'I can't make cake out of sand' and when he says, 'all I have is Championship players'.
"It does not reflect well on the club image. Those players finished ninth in the table last season, it hurts the club financially.
"I am OK with Chris taking all the credit when we win, but at least take some responsibility when we lose. Don't, under the pressure of some losses, say 'everything around me is rubbish'."
"Chris explained why he wanted to resign. He said that he felt the team needed a change, a new voice. We were very clear and said we don't want to fire you, but if you want to resign, you can, but we will not pay you the same money as if we were firing you.
"The emails started between his representatives and our financial guy and we were astonished to find he had asked for £4m to resign.
"We said, 'no way are we going to pay you £4m, you are resigning, we are not firing you, why would we have to pay almost one year's salary?'
On tensions over recruitment in January, Prince Abdullah continued: "We also talked about the January transfer window just before the Southampton game. I felt good after the meeting and I gave him assurances. I went back to Saudi, I felt good.
"Then after we lost to (Crystal) Palace at the beginning of January, Stephen called me and told me Chris wanted to resign. I felt it was my mistake because we recruited how Chris wanted, we spent over £120m."
Meanwhile, with relegation likely to be confirmed at some point next month, Prince Abdullah has stressed that an immediate return to the top-flight will be the Blades' priority, with the club assessing their options during the rest of the season before deciding on Wilder's full-time successor.
Under-23s coach Paul Heckingbottom is currently leading the side on an interim basis for the remainder of the campaign, supported by Jason Tindall.
Prince Abdullah said: "Our first priority is to get back to the Premier League. All options are open.
"We will make a decision soon but we want to see how the team performs for the last eight or nine games of the season."
"We want a coach who will be involved in recruitment, but we have to learn from the mistakes we made before."