The call will be made at a specially convened summit of EU leaders and heads of state in Brussels on Saturday.
At the one-day summit, EU leaders will sign their negotiating guidelines, outlining Brussels' opening position in the Brexit talks due to start in June after the UK general election.
The EU had always insisted on reciprocal guarantees "to safeguard the status and rights derived from EU law at the date of withdrawal".
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However, a document leaked to the UK national press now says, "Such guarantees must be effective, enforceable, non-discriminatory and comprehensive, including the right to acquire permanent residence after a continuous period of five years of legal residence. Citizens should be able to exercise their rights through smooth and simple administrative procedures."
Fears of EU nationals living in the UK have been voiced by MEPs. Parliament's taskforce on citizens' rights, set up in response to those concerns, wrote to the UK Prime Minister Theresa May seeking clarification of Britain's intentions, and calling for EU nationals to be treated "fairly and humanely".
Guy Verhofstadt, Parliament's Brexit coordinator, has condemned May as a political opportunist and said she was motivated by party political considerations rather than the national interest in calling a poll for 8 June.
Writing in the Observer, the former Belgian Prime Minister described the election announced as "an attempted power grab by the Conservative party, who wish to take advantage of a Labour party seemingly in disarray to secure another five years of power, before the reality of Brexit bites".
Verhofstadt, Parliament's ALDE group leader, said putting more Tory MPs in the Commons will do nothing to bolster May's bargaining position when it comes to the talks in Brussels. The latest polls have the Tories about 20 percentage points ahead of Jeremy Corbyn's Labour party.