"As we set out in the Article 50 letter, our view is that withdrawal agreement and terms of the future relationship must be agreed alongside each other", a spokesman for Britain's Brexit ministry said.
Mr Hammond is expected to reinforce his message when he appears on the Andrew Marr Show on BBC1 tomorrow morning, and then his delayed Mansion House speech on Monday.
The UK Government wants the talks to take place in parallel during the Brexit process but both sides have made finding a solution to the issue of citizens' rights a priority.
Prime Minister May has come under pressure to seek a soft Brexit after losing her parliamentary majority last week.
"As we enter negotiations next week we will do so in a spirit of honest cooperation taking a pragmatic approach to trying to find a solution that works both for the United Kingdom and for the European Union 27", Hammond told reporters before a meeting of the 28 EU finance ministers in Luxembourg.
"I will be speaking to her about a renewed commitment by the two governments to work together to ensure that the (Northern Ireland) executive is established before June 29", Leo Varadkar told national broadcaster RTE on Friday, in reference to the deadline to restore the power-sharing regional government.
"We want to end the anxiety facing 4 million citizens", he said.
On Monday, the European Commission insisted it was "fully prepared and ready for the negotiations to start" the process.
Cristiano Ronaldo to win the Ballon d'or !
Real Madrid were crowned winners of the Champions League on Saturday after beating Juventus 4-1 at Cardiff Millennium Stadium. Despite being a global superstar, Cristiano Ronaldo has never forgotten his old mates.
The DUP, under Mrs Foster, is close to striking a deal with the Conservatives that would allow a beleaguered Theresa May to form a minority government in London.
U.K. Brexit Secretary David Davis and his European counterpart Michel Barnier will open negotiations over Britain's split from the European Union on Monday, nearly a year after the country voted to leave.
London-based banking giant HSBC said Friday that it would keep more jobs in Britain depending on the government's approach to Brexit.
"Theresa May must immediately create a cross-party joint Cabinet committee to negotiate Brexit. Everything must go through Barnier", said a third, underlining European Union strategy to keep talks technical for now.
"If the government cannot even secure a deal with the DUP, how on earth can they get a deal with the European Union?" asked MP Alistair Carmichael.
Following more than an hour of talks between May and DUP leader Arlene Foster on Tuesday, May said the discussion had been productive and Foster said she hoped a deal could be done "sooner rather than later".
European politicians also appeared to detect a shift in the mood around Brexit, with France's Macron saying the door was open until the negotiations had concluded for Britain to remain a member of the EU.
"In my experience recently, businesses that look over the garden fence have gone: "Hmm, (the) grass is not quite as dark and unforgiving as you might expect", Andrew told the BBC.