German Vice Chancellor Robert Habeck has said he would wear the multi-coloured "OneLove" armband at the soccer World Cup and see what happened, but he said it was not for him to decide what national team captain Manuel Neuer does.
Habeck's comments came amid a row over the symbol in Qatar, where homosexuality is illegal.
World soccer body FIFA had threatened seven European teams with sporting sanctions if they wore it at the World Cup with the federations backing down.
Germany play their first World Cup match against Japan on Wednesday.
Asked by broadcaster ZDF whether players should wear the armband, Habeck replied: "I am not the media advisor of the DFB (German Football Association) and I am not Manuel Neuer but the opportunity is there."
"I'm a politician trying to do my job properly, but what would happen if it happened now? I would like to know and I would take my chances," he added.
German Interior Minister Nancy Faeser on Wednesday said FIFA's decision was a "grave mistake".
"This is not alright, how federations are being put under pressure," Faeser said during a visit to a German FA event in Doha. "These were not the security guarantees I had received from (Qatar's) Interior Minister" (During her earlier visit in November).
"In today's times it is incomprehensible that FIFA does not want people to openly stand for tolerance and against discrimination. It does not fit in our times and it is not appropriate towards people."
German FA President Bernd Neuendorf, who was criticised for his federation's handling of this case, said the threat of sanctions was not the way to go for such a universal issue.
"Because we all remember the words of (FIFA President) Gianni Infantino," Neuendorf told reporters at the same event. Everyone is welcome."
"That is definitely not a sign of welcome for us if you are led out of the stadium or threatened to be led out of the stadium, so to speak, because you are making a point like this."
"FIFA has expressly stated in its letter that it reserves the right to appeal to the FIFA Disciplinary Committee in the case of such offences, in inverted commas, i.e. the wearing of the armband, which could then impose further penalties, so to speak," he said.
Their comments come after FIFA, cracked down on players wearing the specific armbands in support of diversity at this year's World Cup.
In response to the DFB's decision not to wear it only days after it had said it would, Rewe, one of Germany's biggest supermarket chains, scrapped its advertising campaign with the DFB.