Vingegaard told local TV 2 that he had informed national coach Anders Lund that he was available for the Olympic road race in Paris next year.
"I would really like to race in the Olympics. I have told Anders Lund that if he wants me along, I am ready," he said.
Contacted by the channel, Lund welcomed Vingegaard's offer but did not promise him an Olympic ticket.
"It is not a route that suits me 100%, I believe. And there are many other good Danes, so it may be that he will not choose me," Vingegaard told TV 2.
The soft-spoken champion spoke to media at the City Hall where he appeared on the balcony to celebrate his triumph in front of a mass of fans decked out in red and white, the colours of the Danish flag, or in yellow shirts, as famously worn by the leader in the Tour.
"I'm a big fan of yours, and I am not the only one," Denmark's Prime Minister Mette Frederiksen told Vingegaard during a speech at the City Hall.
"You've won the hearts of all Danes, and we are so proud of you," Frederiksen said.
Vingegaard is the first Dane to become a two-time winner of the Tour de France after last year joining 1996 champion Bjarne Riis as the only other Danish champion.
He moved into the yellow jersey after the sixth stage of this year's race and was then involved in a classic and hugely compelling mountain battle with Slovenian double Tour winner Tadej Pogacar (24).
Vingegaard, however, stamped his authority on the race when he hammered Pogacar by a crushing one minute and 38 seconds on the 16th stage, an individual time trial, to effectively seal the deal.
Vingegaard himself said after the race that it might have been his best day on a bike ever and the Danish fans agree.
Mikkel Feldtmann Hansen (24) had taken the day off from his job as a sergeant in the Danish Royal Guard to come and greet the Danish Tour de France riders.
"It's such an accomplishment to win the Tour de France and it's rare to see Danish sports achieve these big wins and get to be cheered on by their nation," he told Reuters.
Vingegaard and his family were flown to Denmark on Wednesday following celebrations in the Netherlands, home to his team Jumbo-Visma.
"I still think it's hard to believe that I've won the Tour de France two years in a row. That we've won it," Vingegaard said.
Dressed in yellow, Mina Kastbjerg (56) waited for over four hours to celebrate Vingegaard's success.
"We have to show that we celebrate and admire what he has done," she said.
