Downing Street declined to discuss a report on the Politico website that Mrs Merkel rejected the proposal during their meeting in Berlin on November 18.
Amid allegations that ministers were ready to use foreign nationals as a bargaining chip in Article 50 negotiations, which are expected to last two years from March 2017, Mrs May has made clear in recent weeks that she wants to bring forward a deal to guarantee them reciprocal rights to residence, work and healthcare.
But Politico quoted three unnamed people familiar with the talks in Berlin as saying that Mrs Merkel had rejected a swift informal deal to reassure 1.2 million Britons living in Europe and 3.3 million EU nationals in Britain.
In public, Germany has insisted on the EU’s stance that there will be “no negotiation without notification” of Britain’s intention to quit the 28-nation organisation under the terms of Article 50 of the treaties. Mrs May has said she will tender formal notice to leave by the end of March but not before the start of 2017.
Asked about Mrs May’s discussions with the German chancellor, a Downing Street spokesman said: “I’m not going to get into the details of meetings.”
He added: “We have been very clear that we will guarantee the rights of European citizens in this country provided that the rights of British citizens are similarly protected across the EU.
“We have been very clear that we would like to see an early agreement on that, but we need to have a dialogue with the 27 member states.”
The spokesman said: “Negotiations can’t start until we have triggered Article 50, which won’t be until next year. But there is dialogue between the Prime Minister and other world leaders. We have said we would like to come to an early resolution of the issues surrounding the rights of citizens.”
Following talks in Downing Street with Mrs May on Monday, Polish PM Beata Szydlo confirmed that reciprocity of rights for its citizens - almost one million of whom live in the UK - would be a condition demanded by Warsaw during the Article 50 negotiations.
“As for reciprocity in terms of the rights and privileges, they have to be negotiated and there needs to be the right balance,” said Mrs Szydlo.
“This the condition that will certainly be brought up by Poland.”