The 45-year-old German has undergone two operations since sustaining brain injuries after slamming his head on a rock while skiing off-piste in the French Alps resort of Meribel on December 29
The seven-times world champion was in a stable but critical condition until late January and doctors started lowering his sedation level two weeks ago to wake him up progressively.
"As often in such situations no day is like the next. The family is thankful for one's understanding that they would not wish to disclose medical details in order to protect Michael's privacy," Schumacher's agent Sabine Kehm said in a statement.
"As assured from the beginning, we will continue to communicate any decisive new information on Michael's health state. We are aware that the wake-up phase can take a long time.
"The family continues to strongly believe in Michael's recovery and place all their trust in the doctors ... The important thing is not the speed of the recovery but that Michael's healing process progresses in a continuous and controlled way."
Schumacher, who quit the sport in 2012 after a disappointing three-year comeback with Mercedes following an earlier retirement from Ferrari at the end of 2006, won a record 91 grands prix.
(Writing by Gregory Blachier; Editing by Ed Osmond)
