The news outlet said that Norwegian parliamentarian Michael Tetzschner nominated Rose for the award.
"Giving the prize to a consistent defender of freedom of expression, even at a personal cost, would give a sign that those who try to muzzle that freedom through cowardly attacks against civilians, thus undermining peace between peoples, cannot ever succeed," Tetzschner was quoted as saying by the news outlet.
Although the official list of Nobel nominees is kept secret, those authorized to lodge nominations, including parliamentarians, Nobel winners and academics, can announce their choices publicly.
In 2006, the Danish newspaper's controversial cartoons were republished by French weekly Charlie Hebdo, whose Paris headquarters were attacked in early 2015.
After the January 7 attack on the French magazine, Jyllands-Posten is said to be the only Danish daily that has refrained from republishing recent Charlie Hebdo cartoons of Prophet Muhammad.