Fabrice Muamba had a comfortable night but remains in the intensive care unit at the London Chest Hospital.
And his family have asked for visitors to stop heading to the hospital to allow the Bolton midfielder to concentrate on his recovery.
So overwhelming has been the response to Muamba's condition after he suffered a cardiac arrest during his side's FA Cup tie at Tottenham on Saturday, that it has been felt necessary to try and bring a sense of calm to the situation.
It means only members of Muamba's family and Bolton Wanderers FC will be allowed to visit for the time being.
A joint statement released by his club and Barts and the London NHS Trust read: "Fabrice Muamba has had a comfortable night in the intensive care unit at The London Chest Hospital, where the medical team is continuing to monitor his progress.
"Fabrice's family has asked us to thank everyone again for their thoughts and prayers and for the continued messages of support, from which they draw great strength.
"They would also like to thank the media for continuing to respect their privacy."
"To ensure the smooth running of the hospital for all patients - as well as Fabrice's need to concentrate on his recovery - they would request that he receive no more visitors for the moment, outside of immediate family and members of Bolton Wanderers Football Club."
Bolton manager Owen Coyle was once again a visitor this morning, with doubt continuing to linger over Saturday's scheduled Premier League encounter with Blackburn at the Reebok Stadium.
Tonight's trip to Aston Villa has already been postponed, as has a reserve team game due to be played tomorrow night.
However, for all the positivity around Muamba given the progress he has made over the last 24 hours, a debate is now growing over the medical support Premier League players receive.
Premier League chairman Richard Scudamore has promised a review but Manchester City boss Roberto Mancini does not believe what is currently in place is good enough.
"I was really worried on Sunday," said Mancini.
"Today I have read he has improved and I am very happy for him and his family.
"But if you want to know my opinion, it is that here in England, where you have the best championship in the world and everything is fantastic, we need to improve the medical side for the players.
"We need to screen the players often, maybe two times a year and they have to be more accurate because they don't do this.
"When I saw our medical two years ago, I was really worried. I said we need to do them better.
"It is impossible that a young guy could die on the pitch because they didn't do a medical accurately.
"I want all the players, not just ours, to have more accurate medicals.
"And not once a year. Every six months. This is really important for the players because it is totally different today than it was 20 years ago. It is very important.
"What happened to Muamba and other players in the past can't happen again."
The ferocity of Mancini's comments, and the experience of how things work in Italy should ensure improvements are made.
Improvements have been made because when Chelsea goalkeeper Petr Cech suffered a fractured skull at Reading five-and-a-half years ago, manager Jose Mourinho hit out at the delay in the Czech being transferred to hospital.
Chelsea made an official complaint that led to a Premier League and Football Association review, from which measures were introduced that included an ambulance being in place at stadia for the exclusive use of players, and club doctors attending every game.
Speaking at the Sport Industry Breakfast club in London this morning, Scudamore said: "Incidents and events shape policy, shape developments, shape progress.
"What we will be doing is looking at every aspect of what happened and if there are ways and means of improving - just like we did in 2006-07 following the Petr Cech incident - we will do everything we can to make sure we reduce to the point of elimination, if we possibly can, things like that."
Scudamore admitted the Cech incident had been "a wake-up call" for the Premier League.
He added of Muamba: "It's been a difficult three days for everybody involved in the game, particularly those closest to Fabrice.
"The whole of the last three days, we've played out lots of scenarios.
"Let's hope, God willing, that the progress he's making continues to be made and that he makes as decent a recovery as he can.
"In some ways, his life, if it is saved - and let's hope it has been saved - is as a result of the things a lot of us put in place after what happened with Petr Cech.
"If you saw what happened on Saturday, the immediate attention, everybody comes out of this with huge credit, the referee, the match officials, the way the medics were there.
"Jose Mourinho made some strident comments about the treatment that Petr Cech got.
"Everything that we've put in place since helped Fabrice at least have a chance."
