"I think both sides are keen to continue that work at a faster pace than we have done up till now and certainly we would welcome that", she said.
Details of the White Paper are expected to be agreed by Cabinet ministers at next Friday's Chequers away day.
In his invitation letter ahead of the summit, European Council president Donald Tusk proposed the creation of "regional disembarkation platforms" outside the bloc where migrants could be processed, separating refugees from economic migrants.
"We are told that most of the work on the withdrawal agreement is done, but the remaining issues represent some of the toughest questions the Prime Minister must grasp, and negotiations on the future partnership have yet to start in earnest".
But she urged fellow EU leaders to tell their negotiators the United Kingdom should be allowed to continue to take part in schemes like the Prum mechanism for sharing DNA profiles, the Second Generation Schengen Information System - a database of "real time" alerts about certain individuals - and the European Criminal Records Information System.
On the Irish border, the spokeswoman added: "We have never said anything other than it's very challenging".
Mr Rutte said: "I am not losing patience but time is getting shorter and shorter to come to an agreement". If you want to reach a deal in October we need quick progress.
In the remaining 27 European Union member states' joint conclusions on Brexit, agreed in Mrs May's absence on Friday morning, the bloc expressed its concern that "no substantial progress" has yet been achieved on a backstop solution for the Irish border.
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The EU also said there was no agreement yet on Gibraltar, the British enclave at the tip of the Iberian peninsula that is claimed by Spain.
"The European Council expresses its concern that no substantial progress has yet been achieved on agreeing a backstop solution for Ireland/Northern Ireland", the statement continued.
Shortly after Barnier's comments, the EU27 leaders signed off on a joint statement warning in grave terms about the need to prepare for a no-deal scenario.
Talks on the issue are set to begin over Thursday night's working dinner but could stretch into the early hours of Friday if consensus cannot be found.
UK Prime Minister Theresa May has warned EU leaders not to put their citizens' lives at risk by allowing the European Commission (EC) in Brussels to restrict security co-operation with Britain post-Brexit.
The issue has assumed greater political significance in Europe because of the threat to German chancellor Angela Merkel's position over her approach to letting migrants settle in her country.
Irish Taoiseach Leo Varadkar said there should be a degree of "burden sharing" on the transfer of migrants to other countries.
And yet another anti-Brexit campaign is born, with a group of left-wing MPs, campaigners and trades unionists joining together for a nationwide pro-EU tour called 'The Left Against Brexit'.
Among other outstanding issues on the UK's withdrawal agreement, European Union leaders welcomed "further progress" but noted the application of the deal to Gibraltar "still needs to be agreed".