The year-old Nato mission, which provides around 500 soldiers that advise and train Iraqi troops, is currently led by Canada, whose time in charge ends in late 2020.
“We have told Nato we could take the lead” in the operation, Danish Prime Minister Mette Frederiksen told parliament on Tuesday.
“We are doing this because it is an important task that should be followed through in Iraq,” Frederiksen said.
The non-combat mission seeks to bolster Iraq's military and security capabilities, including in areas of medical aid, armoured vehicle maintenance, countering improvised explosive devices and civil-military planning.
The Danish contribution, which first must be approved by a parliamentary vote, will include 13 soldiers to supervise troops and about 70 soldiers to train helicopter forces.
The proposal will be presented at a Nato meeting in London in early December, the Danish foreign ministry said in a statement.