Manager Sabine Kehm did not confirm those reports, but it had been suggested the new illness might have forced doctors to abandon the waking process for now.
But Kehm said in an official statement late on Thursday that the former Ferrari and Mercedes driver "still is in a waking up process".
"The family is thankful for one's understanding that they would not wish to disclose medical details in order to protect Michael's privacy," she added.
"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, nurses and nursing auxiliaries team," said Kehm.
"The important thing is not the speed of the recovery but that Michael's heal process progresses in a continuous and controlled way."