"We are very excited to explore the possibility of a race here in Denmark," F1 chief executive Carey told BT newspaper during his visit on Wednesday.
"We have talked a lot about the importance of our events being at iconic locations that capture the world's interest, and I think Copenhagen does that," he added.
However, there are some hurdles. Private investors are still raising money and trying to secure the full support of government and the community.
And they would prefer an initial three-year race deal.
But Carey said: "Our goal is to have long term partnerships that benefit both sides."
The government, however, is supportive, with industry minister Brian Mikkelsen attending Wednesday's meeting with Carey.
"We had a really good meeting with Chase Carey," he said. "The Danish government is interested in attracting major sporting events, and formula one is definitely that.
"I have told Chase that the Danish government supports this project and is willing to discuss the economics. But we will not be funding the majority."
Carey would not say how close F1 is to a Danish grand prix deal.
"I do not want to say anything about how close we are, as we are interested in many places in the world. But Copenhagen is a special city and we have an opportunity to do something and make this a win-win for everyone," he said.