Respected German newspaper Der Spiegel said that they were contacted by a 35-year-old man who said he caught the crash on camera while filming his girlfriend skiing on the same slope in the French Alps.
The newspaper did not publish the video or mention whether any of their reporters had seen it and told the man to hand the footage to the police.
The witness said that Schumacher was travelling no faster than 20km per hour before his fall.
A French state prosecutor involved in the investigation into Schmacher's crash, Patrick Quincy, told the Associated Press that French investigators were taking steps to obtain the tape but refused to comment further.
Schumacher remains in a critical but stable condition in an induced coma in a Grenoble hospital having suffered severe head injuries in a skiing accident last Sunday.
Schumacher's manager Sabine Kehm also confirmed reports that police were examining footage from a helmet camera worn by Schumacher during the skiing trip on which the accident happened.
"Michael's helmet camera was voluntarily given to the investigating authorities by the family," she said.
"That this should have been done against the wishes of the family is untrue.
"We ask you to respect the continued privacy of the family."