The former Arsenal trainee suffered a cardiac arrest during the weekend's FA Cup Quarter-Final encounter between the two sides at White Hart Lane.
Muamba is said to be making good progress in his recovery and is now able to recognise and talk to family members and friends and breathe independently.
A number of the Spurs players have been buoyed by the improvement in the midfielder's condition, after initially being left distressed by the incident on the pitch where medical staff battled to save Muamba's life.
"It is fantastic news," said Redknapp. "I spoke to [Bolton manager] Owen Coyle late last night and he said they had a great day, better than they ever could have expected yesterday.
"There is still obviously a long way to go, but things are moving in the right direction so it is good news."
Initial reports on Monday suggested the midweek clash between Spurs and Stoke City could be postponed as a result of the horrific incident on Saturday.
However, the encounter is set to go ahead and Redknapp insists the players and staff have been boosted by the improvement in the 23-year-old's condition.
"I think all [the players] have been buoyed by the news that has come through, so things have obviously picked up," he added.
"The news has been fantastic again today and everybody is talking about this morning so it is good.
"I think it affected everybody that saw it. It was just an unbelievable incident and we've never seen anything like that before.
"The whole few days you can't get the lad out of your mind what happened there, but the news is positive and we just keep our fingers crossed now."
