Muamba suffered a cardiac arrest in the first half of the Trotters' FA Cup quarter-final at Tottenham on March 17.
Asked for an update on the player, Coyle said on Thursday: "He has done some short periods of walking down the corridor he is in as part of the unit, staying in intensive care.
"He is taking steps, talking and has that big smile which we love to see, so he is certainly progressing the right way."
He added: "My chairman Phil Gartside was there yesterday with our club doctor Jonathan Tobin, and our club chaplain Phil Mason will be there today to continue the support from the football club.
"A couple of players have been sending him messages and we are keeping in touch. It has been great to see that smile and he continues to get better.
"We have to stress that he still has a long way to go, but the improvement has been remarkable and long may that continue."