The former England player is the fans' choice to take over from the beleaguered Francis, who had supporters calling for his resignation following Saturday's 7-1 defeat by Nottingham Forest, the Hillsborough club's heaviest League defeat.
Francis is insisting he will continue to "grin and bear it" as he prepares for this Saturday's fixture against Leicester.
Waddle, who has declared an interest in management once his playing career is over, insisted: "I don't feel a rush to go into management."
He also defended the track record of his manager, despite a recent run of seven defeats in the last nine games. "We've been to Wembley, got into Europe and had good Cup runs in the last few years," Waddle said.
"This is the first time we've had a patch like this. Surely the fans can get behind us for 90 minutes on Saturday. It's an important game and we need the points. A lot of players are struggling, confidence-wise. The last thing they want is people chanting or screaming at them that they're rubbish."
He added: "Obviously we've got to do better than last Saturday. I still think everyone tried. No one was shirking. We were playing a good side.
"We appreciate the fans paying good money to see us - now we really need them to get behind us."
The Hibernian striker Darren Jackson, who collected his first full cap for Scotland against Russia last week, is acquainted with pressure of another kind.
Scottish Cup semi-finals rarely come as intense as a meeting with Celtic, and at Ibrox on Friday Jackson will have his cool nerve thoroughly tested. His ability to maintain grace under pressure was evident when he scored a last-minute goal for Dundee United in the 1991 Scottish Cup final, yet he still finished on the losing side.
"Obviously there's going to be pressure but that's what type of a game the semi-final is," he said. "The advantage is that it's an enjoyable pressure - one that I've had before and one that I want to have again. The players love it and I especially am looking forward to the game because there's going to be a fantastic atmosphere."
Despite his predictions of triumph, Jackson is well aware of the vagaries of Cup football. He was part of the Dundee United side that lost 4-3 to Motherwell in 1991, and Jackson is determined to conquer that disappointment and bring back the Scottish Cup to Hibernian for the first time in 93 years.
"Losing in 1991, especially after scoring, was a huge disappointment," he admitted. "Chances like that don't come too often and so I'm looking to get back there and make amends."