The Danish PM's remarks came after British Prime Minister Theresa May gave a much-anticipated speech in which she advocated for a so-called ‘hard' Brexit – a clean break from the EU and not a “half-in, half-out” model.
“If the UK wants to completely pull out and have a proper trade agreement, then we need to look at it. From a Danish perspective, we want to enter into this constructively,” Rasmussen said after May's speech.
“We have an enormous interest in cooperating with the UK on trade, combating terror and education in one another's countries,” the Danish PM added.
Danish opposition leader Mette Frederiksen of the Social Democrats also said it was in Denmark's best interests to “remain as close [to the UK] as possible”.
The tone in Denmark was decidedly warmed than that in France, where the nation's finance minister accused the British government of "improvising" its handling of Brexit and "flip-flopping".
Tuesday's speech saw May announce her desire for a full break from the EU which entails leaving the single market in order to have full control over immigration.
She said the UK "cannot possibly" remain in the European single market, because if it did remain it would mean "not leaving the EU at all".
European Council President Donald Tusk tweeted after May's speech that the EU's other 27 member states were "united and ready to negotiate".