"For us it's not a question of generosity, it's a question of continuity and fairness," Stefaan De Rynck, a senior aide to chief EU Brexit negotiator Michel Barnier, said at a seminar in Brussels.
Brussels has made the future of three million EU citizens in Britain and one million Britons in Europe a priority, insisting they should be allowed to keep their rights to live, work, study and claim welfare benefits.
London will then make a detailed proposal next week, Davis said.
Reports in British newspapers this month said May would make a "big generous offer".
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But with EU citizens already guaranteed these rights across the 28-nation bloc, De Rynck said "there is nothing particularly generous about this issue."
"Let's wait for that paper... There may be some common ground. No doubt there will be differences. We will need to know these differences very soon so we can start the negotiations."