Incumbent NATO Secretary General Jens Stoltenberg's term is scheduled to end in late September following multiple extensions. Another extension is also a possibility if the allies fail to agree on a replacement, media reported.
Frederiksen fits several criteria NATO leaders consider important in a new chief, according to the reports. This includes being a European, a head of government, a strong supporter of Ukraine and a woman.
"I think she is a serious candidate," a western European diplomat has been quoted as saying.
A senior diplomat from Central Europe confirmed the Danish leader "is indeed considered seriously by a number of bigger allies."
Frederiksen has received an invitation to visit the White House on June 5 in what many reportedly see as Washington's impending go-ahead for the role traditionally reserved for Europeans.
There are reportedly also arguments against her, however. Some point out that NATO has already had a chief from Denmark, Anders Fogh Rasmussen, who held the post from 2009-2014. Furthermore, Denmark's defense spending is still below the targeted 2% of the GDP, which diplomats fear might send a wrong signal, a Central European diplomat told media.