But a flat-out rejection of the proposal by the populist Danish People's Party (DF) is likely to leave the Conservatives with an uphill task, reports broadcaster DR.
DF leader Kristian Thulesen Dahl told DR on Tuesday that his party will not support any proposal that would see reduction in the number of Danes falling in to the country's highest tax bracket.
The Conservatives therefore hope to persuade DF to reform so-called extra tax (ekstra-skat) rules at autumn meetings between the parties.
Although even this will be a difficult task, it remains a top priority for the party, the Conservatives' political spokesperson Mette Abildgaard told DR.
“I see this as a clear signal from the Danish People's Party that this is not their cup of tea, and if they are to go along with it they must be given something in return. I completely understand that's how it works. But let's give it a chance. I would also appeal to the Danish People's Party to see if we can meet in the middle,” Abildgaard said.
One of the aims stated by the coalition when it formed in November 2016 was to reduce the number of people paying top tax rates.
This would mean the threshold for the top tax bracket being raised from the current annual income of 480,000 kroner (64,500 euros).
Abildgaard admitted that a failure to implement this would constitute a defeat for the conservatives.
“If we can't get this passed, it would be a real shame. No doubt about that. But that's how Danish politics works. There are many parties that have to work together to find a compromise. But I have certainly not given up hope,” she said.
The Social Democrats, the largest opposition party, have also confirmed their opposition to reduced top-level taxation.
“Money can only be spent once, and we think it makes a lot more sense to invest in a proper social welfare society, rather than spending it to give tax breaks to the people that earn the most,” Social Democrat political spokesperson Nicolai Wammen told DR.
“I am glad the Danish People's Party supports our point of view, since that makes it impossible for (Prime Minister) Lars Løkke to push through tax breaks. We have made it clear we think that is a very bad idea,” Wammen added.