The F-16s will be part of an expanded NATO air policing mission.
Patrols are expected to begin on May 1 and continue until the end of August, said public broadcaster DR.
The Danish contribution was "an attempt to show solidarity with the Baltic countries in the current situation", it said.
A spokesman for the Danish foreign ministry said he was unable to confirm the information before a meeting in parliament today morning.
France last week offered to send four fighter jets to the Baltic states and Poland to boost NATO air patrols over the region.
It followed a decision by the US to bolster military cooperation with Poland and Baltic states to show solidarity after Russia's intervention in Ukraine.
The mostly symbolic steps to expand aviation training in Poland and step up the US role in NATO's air patrols were designed to reassure alliance partners in central and eastern Europe following alarm at Russia's actions in Crimea.