His side will be returning to action in the Barclays Premier League against Stoke on Wednesday night
On Monday night, it was confirmed the 23-year-old was able to answer questions and speak in both French and English, which represents a dramatic improvement for the Bolton midfielder, whose heart stopped for two hours following his collapse during the first half of his side's FA Cup quarter-final at White Hart Lane on Saturday evening.
Spurs' players and coaching staff alike were all moved by the experience, with both counselling offered by the club as well as the opportunity for heart tests at the training ground in Chigwell.
Redknapp hopes the positive news coming from the London Chest Hospital concerning Muamba will allow focus to return to football tomorrow night, when Spurs will aim to get their Premier League campaign up and running again following three straight defeats.
"I spoke to (Bolton manager) Owen Coyle late last night [Monday], and he said they had had as good a day as could have been expected," said Redknapp, who revealed Stoke manager Tony Pulis had offered support to postpone Wednesday's game if deemed necessary.
"There is still a long way to go, but things are moving in the right direction and we will keep our fingers crossed for the boy.
"All the lads are buoyed by the news which has come through, things have obviously picked up.
"We had people come in yesterday, but the lads are fine at the moment."
The Tottenham manager added: "Sometimes the best thing is to get back on the bike if you fall off, and we need to do that, we need to get going again.
"We need to play tomorrow [Wednesday] night and we are ready to play.
"It will be a very tough game and we need to be ready to play, if we are not, then we will be in trouble with Stoke, that is for sure.
"The players were fine when they trained yesterday morning, and I am sure they will be fine today and ready to play tomorrow."
Redknapp, though, stressed he would manage the situation carefully.
He added: "If there is anybody who today feels they are not in the right frame of mind to play, then obviously I would not play them. But if everybody is okay, I will pick a team which is the best to try to win the game."
Spurs' recent slump in form, which started with a 5-2 defeat at Arsenal, has allowed their north London rivals to close up on third place, with now only one point separating the two clubs.
Chelsea are also within striking distance of Spurs, who at one time looked set to challenge Manchester City and Manchester United for the title.
Redknapp, though, remains confident his squad can soon get back on track.
He said: "We have had a run of not good results, but they have not been bad performances.
"We are not playing badly, but we need it a result and want to be in form tomorrow.
"If we don't win, then things are really getting a bit tight. It has closed up and you have to make sure we try to pick up three points."
Spurs are likely to face former striker Peter Crouch tomorrow. The England international joined the Potters in a £10 million deal at the end of August.
Redknapp also had Crouch with him at Southampton and Portsmouth.
"Crouchy has made an impact wherever he has been," he said.
"He did a great job for us here, and also for me when we were at Portsmouth.
"I was sorry to lose him and it was not a case of wanting to get rid of Peter. We were taking Emmanuel Adebayor and I could not keep everybody.
"Peter moved on, but you would have him any day, he is a top player and a great lad as well."