ROME - Britain's future ties with the European Union may not mirror any of the existing relationships between non-EU countries and the bloc, Prime Minister Theresa May said on Wednesday after meeting her Italian counterpart.

The Financial Times reported on Wednesday that international trade minister Liam Fox was pressing May to pull out of the EU's customs union, an area in which there is free movement of goods but where tariffs are imposed on external borders.

Fox has said a free trade agreement with the EU was more likely than staying in the customs union, which could restrict Britain's ability to negotiate lower tariffs with other trading partners, the Wall Street Journal reported on Tuesday.

Asked about the comments, May said Fox had simply been setting out the technical and legal position about the differences between customs unions and free trade agreements.

"I'm looking at this with an open mind," she told a news conference following the meeting with Italian Prime Minister Matteo Renzi in Rome.

"I think we should be developing the model that suits the United Kingdom and the European Union. Not adopting, necessarily, a model that is on the shelf already."

May said last month's referendum, ahead of which immigration was a key part of the debate, had sent a clear message that freedom of movement from the EU could not continue as it had in the past. But Britain also needed to get the best possible deal on trade in goods and services, she said.

The new British leader, who has embarked on a tour of European capitals since taking office earlier this month, has said Britain needs time to prepare for negotiations with the EU, and so will not trigger the formal exit process this year.

Renzi said while he respected Britain's vote, a clear time frame was needed for Brexit.

"Brexit is Brexit, we cannot open again the discussion, because if we open again the discussion we give the message against the idea of democracy," he said. "Italy will do its utmost to collaborate and support the process ... But it's important to have a vision and precise timeline for the process" of Britain leaving the EU."

May also said she hoped to be able to address the issue of the rights of EU nationals living in Britain and British citizens living in the EU early on in Brexit talks.