Formula One chairman Chase Carey discussed the proposal with the city's mayor and the Nordic country's business minister during a visit to Copenhagen on Wednesday.
"We're excited about the opportunity to explore a potential race here in Denmark... I think Copenhagen represents the type of location that we think can really provide a great platform," Carey told journalists, but said no final decision had yet been made.
Liberty Media, Formula One's new American owners, have big plans to reshape the sport and are targeting new venues in key markets, including the United States and Asia.
A Copenhagen race would open the gates to the rest of Scandinavia, said the consortium behind the initiative, which is led by former minister Helge Sander and Lars Seier Christensen, co-founder and former CEO of online trading platform provider Saxo Bank.
"They don't just see it as Copenhagen but as all of Scandinavia which is a potential market for them," Christensen told a press briefing ahead of Carey's visit.
The estimated budget is 300-500 million Danish krone (35.73-59.54 million pounds) per race while the expected income from spectators including tickets is seen at 1-2 billion Danish krone ($160-320 million), Christensen said.
Kevin Magnussen, who races for the U.S.-owned Haas team, is the only Danish Formula one driver and has a big following in the country.
"Scandinavia has been a great part of our sport and having local drivers is always a plus," Carey said.
He added that the bridges and water in Copenhagen would provide great television pictures.
TV is crucial to Formula One which had a cumulative television audience of 1.4 billion for all F1 programmes broadcast in the top 20 markets last year.
A key hurdle will be to get approval from the city council for the 4.6 kilometre long route through the old city centre, where an estimated 107,000 spectators could be seated.
Copenhagen is usually promoted as a 'bicycle heaven' with around 150,000 people cycling to work everyday.
Denmark has never hosted a Formula One race and the only one ever held in the Nordics was the Swedish Grand Prix at Anderstorp, which fell off the calendar in 1978 after the death of local heroes Ronnie Peterson and Gunnar Nilsson that year.
(Reporting by Stine Jacobsen in Copenhagen, additional reporting by Alan Baldwin in London; Editing by Christian Radnedge)
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