The original tie, on Saturday March 17, was abandoned after 41 minutes following the Bolton midfielder's on-pitch collapse at White Hart Lane with a cardiac arrest that almost proved fatal.
The 23-year-old's life was saved thanks to rapid and expert medical care and fans around the country have been buoyed by a series of encouraging progress reports, although Muamba remains in intensive care.
And with Bolton having returned to competitive football by beating local rivals Blackburn Rovers 2-1 in the Premier League at the weekend, Redknapp is optimistic Tuesday's match will no longer be an emotional chore for both clubs.
"It would have been but everybody is just so pleased with what has happened," Redknapp said of a tie where the winners will meet Chelsea in the last four of the Cup at Wembley.
"I don't want to get ahead of myself with Fabrice but from where we were from last Saturday (March 17) to where we are now is just a miracle.
"When you saw that boy go up that tunnel and I spoke to my club doctor, he was gone.
"We all felt he wasn't going to make the night or make it to the hospital," added Redknapp, who said he'd been in regular touch with Bolton counterpart Owen Coyle regarding Muamba's health.
"So when the news started coming out, and I spoke to Owen every day, it has just been fantastic.
"It is almost a miracle that your heart can stop that long (Muamba was "effectively dead" for 78 minutes) and he can come round.
"So I think we can move on now. We want to play on Tuesday night and both teams are going to want to win, obviously."
Coyle admitted he could not be sure how his players would react to returning to White Hart Lane but Bolton will go into the tie on the back of a win at home to relegation rivals Rovers.
Bolton players will also use the occasion to visit Muamba at the London Chest Hospital, where he remains in intensive care, but at least the Trotters no longer have to contemplate pulling out of the FA Cup.
"The positive is that Fabrice is getting better," Coyle said. "If he had not been, it would have been a different conversation we would be having.
"I can't tell you how we will cope with going back until we get there.
"As much as we felt ready to play (against Blackburn), until they (the players) cross that white line, you don't know how they are going to react."
Defender David Wheater, who scored both goals against Rovers, added: "It will be difficult but now we know he's getting a bit better we can go there and play for him (Muamba), like we did against Blackburn.
"If we win, we're at Wembley and I think Fab would want us to do that."
For Coyle, Tuesday's tie will also a chance for the club to show its appreciation to all those who've helped Muamba.
"Tottenham Hotspur are an absolute credit to themselves in terms of their medical staff who acted together with (cardiologist) Andrew Deaner, the supporter who came out of the stand," he said.
"It gives both teams the opportunity to thank everybody for their support of Fabrice. Because it is a live game, as it was last Saturday, it is a chance to show everybody worldwide our thanks for the support they have shown."
Ledley King could replace William Gallas in the centre of Tottenham's defence, having been left out of Saturday's goalless league draw at Chelsea.
King played in the midweek draw with Stoke City but rarely appears in two games in the same week because of a chronic knee problem.
"He was fit but I went with Gallas," Redknapp explained. "Playing Ledley could have wiped him with two games in quick succession. It might have damaged his knee so badly we couldn't see him again this season."
Source: AFP
Source: AFP