Denmark women are on strike and did not play their friendly against the Netherlands on Friday.
The DBU offered a temporary deal to the Danish Professional Footballers Association (PFA) on Saturday but an agreement could not be reached.
The Danish PFA sent two proposals to the DBU on Sunday - both were rejected.
"It is very frustrating trying to make ends meet when you face an FA which does not actually want to negotiate," said Danish PFA president Jeppe Curth.
"The players are extremely focused on reaching an agreement, so they can play the game against Hungary on Tuesday, and they hope the FA is as well."
DBU communications manager Jakob Hoyer told BBC Sport the association would "have to find other players or withdraw" from Tuesday's World Cup qualifier.
"It's a very positive thing the men have done but it is not part of our negotiations," he added.
What is the dispute?
The negotiations, which are understood to have been ongoing for the past nine months, are focused on whether the women's national team players are employed by the DBU.
In the new deal put forward by the Danish FA, the women national team are no longer classed as employees, which the Danish PFA strongly oppose.
The DBU set a deadline of 13:00 local time on Saturday for the players to accept their temporary offer but an agreement could not be reached.
"On Sunday we sent two new proposals to the Danish FA," Curth said in a statement.
"The last one included an offer from the players of the men's national team, who offered 500,000 DKK (£60,000) a year from their agreement with the DBU to the women's national team instead.
"This was on the condition of the Danish FA securing the same basic rights for the women in their agreement as the men have in theirs. The DBU has unfortunately decided to reject both these offers."