The Austria Press Agency APA said on Thursday Morgenstern would move to a clinic in Klagenfurt, raising hopes he could still take part in next month's Winter Olympics in Sochi.
"It is going surprisingly well for him," Josef Obrist, chief physicist at the Salzburg hospital where the 27-year-old was being treated, told APA.
"We simply want to let him regenerate and rehabilitate. There is a little bit of a memory block but nothing out of the ordinary," he added.
Morgenstern was injured during a training accident at Bad Mitterndorf, Austria, on January 10 after he lost his balance in the air, turned over and landed on his back and head.
It was the second heavy fall for Morgenstern this season after he crashed on the snow following a jump at the World Cup in Titisee-Neustadt, Germany, on December 15.
Then, he suffered several bruises, face cuts and a broken finger but recovered quickly and finished runner-up to fellow Austrian Thomas Diethart in the Four Hills Tour last week.
Morgenstern won two Olympic titles in the individual and team large hill event in Turin in 2006 and a team large hill gold in Vancouver in 2010.
On Monday, officials announced that he was progressing well and team doctor Juergen Barthofer said it would be two weeks before any decision could be made on whether Morgenstern could compete at the Sochi Games which start on February 7.
- Sports & Recreation