It was confirmed by Schumacher's management on Monday that the 45-year-old has left the hospital in Grenoble where he was being treated for serious head injuries.
The seven-time F1 champion had been in a medically-induced coma since he hit his head on a rock while skiing off-piste in the French Alps on December 29.
"I always keep him in my thoughts and prayers," The Telegraph quotes Hamilton as saying. "It's a real positive to hear that there's been some progress.
"I've been trying to keep an ear out for what's going on but not really hearing much improvement. To hear that he's really in that wake up phase is really encouraging. It's exciting for the next steps. Hopefully this is the first onto the new ladder."
Schumacher has been taken to an undisclosed location to continue the rehabilitation process.