Muamba suffered a cardiac arrest in the first half of the Trotters' FA Cup quarter-final at Tottenham on March 17, with the game subsequently being abandoned.
Asked on Thursday morning for an update on the player, Coyle said: "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."
The former England Under-21 international, who turns 24 on Friday, received treatment on the pitch before being carried off on a stretcher and rushed to the London Chest Hospital.
It has emerged that it took 78 minutes for his heart to start working on its own again, but Muamba has made incredible progress since then and last Friday a picture of him sitting up in his hospital bed and smiling was posted on Twitter.
Coyle 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."