UEFA, as organisers of the event, will have the final say.
The Munich city council accused Hungary "of following the example of Russia's homophobic and transphobic legislation."
"This legislation represents a new mark in the invisibility and disenfranchisement of lesbians, gays, bisexual, transgender and intersex people (LGBTI) and adds to the systematic restriction of the rule of law and fundamental freedoms that have been practiced for years in Hungary," the council said.
In a positive sign for Munich's application, UEFA called off an investigation into German captain Manuel Neuer's wearing of an armband in rainbow colours for his team's opening group games against France and Portugal. He also wore it in the 7-1 warm-up win over Latvia before the tournament.
German broadcaster NTV reported Sunday that UEFA was investigating Neuer's use of the armband and that the German football federation could face a fine because political symbols are not permitted.
However, the team announced on Monday that it had received a letter from UEFA saying "the armband has been assessed as a team symbol for diversity and thus for a 'good cause'".
Meanwhile, the local council said Munich "is committed to diversity, tolerance and equality in sport and in society as a whole."
But not everyone agrees.
Uwe Junge, a politician with the far right AfD party, was chastised by party leader Alice Weidel for "going too far" with a since-deleted post on Twitter in which he used a homophobic slur to describe Neuer's rainbow armband.
The Munich stadium has been lit in rainbow colours on several occasions since the first time on the night of July 9, 2016, to celebrate Christopher Street Day.