(Adds quotes on single market, financial services)
DUBLIN, Jan 25 (Reuters) - Ireland would like Britain's relationship with the European Union to be closer than that of non-member Norway, but it will have to be a specific agreement as there is no precedent for the relationship, Ireland's prime minister said on Thursday.
"I think it will be a specific agreement for the United Kingdom. Of course as Ireland we want that to be as close as possible - we would have it 'Norway-plus' but I think we have to get into the detail now of what that means," Leo Varadkar told Bloomberg Television in an interview in Davos, Switzerland.
Norway is part of the European Union's single market, but not the customs union.
The EU's chief Brexit negotiation Michel Barnier in December said the future free trade agreement between the European Union and Britain would have to be along the same lines as the one the EU has with Canada.
But Varadkar said that neither the Norwegian model nor the Canadian model would fit the United Kingdom.
"It's difficult to compare it to Norway, which is a relatively small country... or a country like Canada, which is on a different continent," he said.
While Britain has repeatedly said it will not remain in the EU customs union or single market, "perhaps we can negotiate something that isn't very different to that," Varadkar said.
Such a deal would, however, require the United Kingdom to realise that it cannot cherry pick benefits of EU membership without the corresponding responsibilities.
Access to European markets for London-based financial services firms would depend on what the UK might give in return, he said. (Reporting by Conor Humphries Editing by Jeremy Gaunt)