Prime Minister Lars Løkke Rasmussen gave the idea credibility when he called it a “real option” in a book published last week.
With the exception of wartime unity governments, the two traditional rival parties have only governed together once before, for a brief period the late 1970s.
Social Democrat leader Mette Frederiksen subsequently moved to reject the possibility saying that the parties disagreed on too many areas for a cross-aisle government between the two to work, Ritzau reports, although a report by newspaper Politiken last week highlighted the fact that they have voted the same way in over 90 percent of the 824 legislative votes conducted in parliament over the last four years.
Nevertheless, voters also appear unconvinced by the prospect.
A poll conducted by Voxmeter on behalf of Ritzau shows 32 percent of voters in favour of the proposal and 48 percent against it, while 20 percent said they did not know what their view was.
Liberal voters were more open to the idea than their Social Democratic counterparts, however.
65 percent of Liberal voters approved of a potential partnership between the parties, compared to just 27 percent of Social Democrat backers.