The 23-year-old's heart has begun beating without the aid of medication and is able to recognise the family members that are tending to him as he recovers from cardiac arrest
A friend of Muamba's had earlier tweeted that the midfielder was able to speak short phrases in English and French.
The former England under-21 international remains critically, and will remain in intensive care as his condition improves.
A statement from Bolton read: "Fabrice Muamba remains in intensive care at The London Chest Hospital. He is continuing to show signs of improvement this evening.
"He is currently able to breathe independently without the aid of a ventilator. He has also been able to recognise family members and respond to questions appropriately.
"These are all positive signs of progress. However, his condition remains serious and the medical staff in intensive care will continue to monitor and treat him.
"His family and club would like to thank the media for continuing to respect their privacy at this time."
The 23-year-old suffered a cardiac arrest in the 42nd minute of the Trotters' FA Cup clash with Tottenham on Saturday and received CPR treatment on the pitch before being taken to hospital where he was resuscitated after going two hours without breathing.
Family and friends of the former Arsenal man have visited the hospital, along with staff from Bolton including manager Owen Coyle, chairman Phil Gartside and captain Kevin Davies.