“We have a favourable attitude to increase our troops in Afghanistan if necessary, but we haven't reached the conclusion yet,” Claus Hjort Frederiksen said.
“I can generally say that we are positively thinking of adding our presence in Afghanistan,” he added, speaking in the Danish capital alongside Pentagon chief Jim Mattis.
Denmark currently has about 160 troops and support personnel in Afghanistan, according to a defence ministry website.
The BBC on Tuesday reported that Nato had asked London for an unspecified number of additional troops for Afghanistan.
US authorities have written to Nato allies and partners about the future of the alliance's presence in Afghanistan.
“Allied leaders will consider future contributions at our meeting in Brussels later this month, and the issue will be examined in further detail by defence ministers in June,” a Nato official told AFP.
“It is important that Nato continues to provide the right level of support to the Afghan security forces as they stabilise their country.”
The Pentagon is widely expected to formally request thousands of extra US troops to head to Afghanistan to push back against a resurgent Taliban and help beleaguered local troops.
According to US media, the Pentagon will ask for 3,000 to 5,000 more soldiers, mainly to be assigned to advise and train Afghan military and police.
Mattis did not discuss the matter but said the future of Afghanistan's security lies with Kabul's ability to improve governance.
“When a government wins the affection, respect and the support of their people, then no enemy can stand against them,” he said.