But following the Prime Minister's failure to win a majority in the General Election, Mr Hammond, who is seen as one of the most pro-EU members in the Cabinet, will attempt to change Ms May's mind on leaving the customs union, according to The Times.
The European Parliament's chief negotiator has demanded Britain clarifies its position and abandons its plans for a "hard" Brexit.
Theresa May needs the 10 DUP MPs to govern without a majority after her gamble on a snap election backfired.
Britain's negotiations with the European Union over its exit from the bloc begin on Monday and stand to be complicated by the surprise loss of Prime Minister Theresa May's parliamentary majority in a national election last week.
"If the Government cannot even secure a deal with the DUP, how on earth can they get a deal with the EU?"
A Treasury spokeswoman declined to comment on the report.
London has said it wants the Barnier-Davis talks to start as scheduled next Monday, but since Thursday's election it has not formally committed to the date.
The government also said the extra legislative time was needed to pass its domestic agenda.
But a deal with the DUP also risks destabilizing Northern Ireland by increasing the influence of pro-British unionists.More news: Russian Federation dominate New Zealand in Confederations Cup opener
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"It includes money, they want to talk about that, we think it should come later, and Northern Ireland".
May needs the support of the DUP to govern, after she lost her parliamentary majority in the United Kingdom election.
Irish nationalist party Sinn Fein said the prospect of a British agreement with the DUP was causing anxiety and fear.
Foster said her party would go into the talks "with the national interest at heart".
Former Prime Minister David Cameron said May needed to listen to rival political parties, and that there would be pressure for a softer Brexit. Divisions over Europe helped sink the premierships of Margaret Thatcher, Major and Cameron, and many of her lawmakers and party membership support a sharp break with the EU.
Under the "no deal, cliff edge" withdrawal, the United Kingdom would leave the European Union and implement World Trade Organisation rules which would mean tariffs on goods exported from the United Kingdom to the European Union - which amount to 44% of United Kingdom outward trade.
The veteran conservative predicted that Britain would regret its departure from the bloc at some point in the future.
The EU's executive Commission said in a statement Friday that the first round of negotiations in Brussels will be part of a "sequenced approach to the talks".