Theresa May says Britain will strengthen ties with European nations but insists a post-Brexit model must suit the UK and Europe.
The Prime Minister says she wants to guarantee EU citizens' rights in the UK but will be seeking the same guarantee for Britons abroad.
Theresa May said she hoped to be able to address the issue early on in Brexit talks to provide certainty for those living in Britain and UK nationals living in EU countries.
She reiterated that the UK must be able to control immigration, but also get the "best possible deal" for its economy.
She said: "I want to be able to guarantee their rights in the UK. I expect to, I intend to. But it's not possible if the rights of UK nationals living in other EU states are not guaranteed.
"I'm looking at this with an open mind. 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."
Mrs May was speaking alongside Italian Prime Minister Matteo Renzi in the latest stage of her whistle-stop tour of European leaders.
Mr Renzi said the negotiations must be as "efficient as possible" and called for a specific timeline to be set out.
He added: "It's in everybody's interest to succeed in the end, to succeed in having a vision or a specific timeline which will make this pass easier.
"Of course we are saddened by this and we, to a certain extent, understand the public opinion.
"It's a decision that was made by the British people and we respect it, however painful it is. Now we have to deal with it with common sense."
Italy is the UK's eighth largest export market and trade in goods was worth £24bn last year, Mrs May said.
She told the news conference she had chaired the first meeting of a Cabinet committee on exiting the EU to "plan for an orderly departure".
The Prime Minister has been accused of using EU nationals living in the UK as "bargaining chips".
It comes as MPs on the Home Affairs Select Committee warn that Britain could face a "surge" in migration from EU nationals rushing to come to the UK before Brexit restrictions are imposed.
They urged Mrs May to impose a "cut-off date" for them to settle permanently in the UK to avoid a spike in applications.