The seven-time Formula 1 champion had been in a medically-induced coma for almost six months after suffering a skiing accident in France, but was moved to a hospital near his Switzerland home on Monday.
A source close to the Schumacher family told The Independent: "The transfer doesn't mean that his condition improved markedly in the last few weeks. But he no longer needed to be in intensive care and a programme of rehabilitation is now underway.
"He is still going in and out of consciousness but he is having more moments of consciousness more regularly than in April.
"He certainly can't talk but there is some degree of communication. His doctors and family speak to him but he gets tired very quickly and needs a lot of rest. So this is kept to a minimum."
The 45-year-old German sustained severe head injuries after falling at the resort of Meribel in December.