Muamba, 23, remains critically ill at the London Chest Hospital after collapsing in the first half of Bolton's FA Cup quarter-final tie at Tottenham Hotspur.
He required CPR and defibrillation from the physios and medics on the scene, while Dr Andrew Deaner, a Tottenham fan who is a consultant cardiologist at the London Chest Hospital, raced onto the pitch to help assist Muamba after his heart stopped.
Bolton manager Owen Coyle and chairman Phil Gartside are both by Muamba's side, but he remains anaesthetised and the hospital said on Monday that the former England U21 international "remains critically ill".
Davies, who went with Muamba to hospital on Saturday night, expressed his and the club's thanks to the medical experts who have helped Muamba in his battle to stay alive.
"It's been a difficult time for everyone involved with the club, I think for everyone involved with football really," Davies told Sky Sports News. "It's so tragic it could happen to someone like Fab.
"We're hopeful that he can pull through and I just want to say, on behalf of his family and everyone at the club really, a big thank you to everyone who was on the scene, the paramedics and our own medical staff.
"I went down to the hospital with the manager and the physios and the doctors and the amount of people and doctors that were turning up and running around down there trying to get Fab sorted out, it was amazing.
"There's no doubt in my mind if it wasn't down to all those people we wouldn't even be in this situation so we're all thankful to them that they've given Fabrice a bit of hope.
"As you can imagine it's been sleepless nights, with what we saw on the pitch. I've been in constant contact with the manager and the doctor, who I've asked to keep me informed so I can let the players and friends and family know what the situation is.
"You're half expecting the phone to ring, with what we saw. But Fabrice is fighting and like I said, we're all holding out and hoping he can pull through."
There have been suggestions that Bolton players are not comfortable facing the prospect of a rearranged cup game at Spurs.
Davies admitted that Bolton's next game was the last thing on his mind. He said: "Any of those questions are irrelevant at the minute."
Muamba made his professional debut under Arsene Wenger and the Arsenal manager has joined so many other figures in the world of football by paying his own tribute to the 23-year-old.
"This is of course a massive shock to us all and we just hope that Fabrice will pull through safely," Wenger told the club's official website.
"You pray that the damage will be repaired and that Fabrice will come out healthy and we will see his smile again. That is all you wish for.
"As a man, Fabrice has a positive attitude towards life, he is full of determination and has a great desire. Everyone at Arsenal has huge respect for Fabrice. Even after he left us, he often passed by to say hello and speak about how it was going for him. We feel very deeply attached to him.
"He is what you would call a committed player. His hunger and determination was so big. When he was younger, he had massive players in front of him at Arsenal, but I felt he had reached the level to play in the Premier League, so we let him go and he has proved his quality.
"A football player always remains attached to where he was educated. Fabrice had his friends from childhood here and they remain your friends forever. We are all thinking of Fabrice, his family and everyone close to him.”