"This is a certain relief," she is quoted by Spain's El Mundo. "For the family, the situation is calmer.
"This is the start of a long, long period, but thankfully less difficult now.
"The most dangerous moment has passed," added Kehm.
The SID news agency, and the major German daily Bild, quoted an unnamed source close to the former Ferrari and Mercedes driver as confirming that there was indeed a "slight improvement" in Schumacher's condition.
Bild said it was a dramatic change from the unofficial news on Friday, when the seven time world champion "looked as though he had lost the fight for life".
A brain scan on Friday, the newspaper added, was "catastrophic".
"His condition is still critical," Kehm was quoted by Sky Deutschland television, "however it has stabilised over the weekend.
"The danger to his life is no longer immediate."
Italy's La Gazzetta dello Sport quoted Kehm as saying the family had "heaved a sigh of relief" early this week.
And a doctor treating Schumacher, Jean-Francois Payen, was quoted as saying: "While we emphasise that the danger has not yet passed, it is certainly no longer acute."
RTL reporter Felix Gorner said: "Sabine Kehm has just told me on the phone that, for the first time, Michael Schumacher is no longer in imminent danger of death."
An official statement issued by the treating hospital in Grenoble also sounded more positive than earlier bulletins.
It said Schumacher's "clinical state" is now "stable". "However," the statement added, "the medical team in charge of his care underlines that they continue to consider Michael's condition as critical."
Later, Schumacher's manager Kehm played down those reports that had quoted her as saying her boss' life is no longer in danger.
"I cannot confirm any expressions that he is no longer in danger," she said. "I refer you to the statement that was issued by the doctors."