Five representatives from grassroots organisations will attend the meeting later this month with Michel Barnier, along with three representatives of UK nationals living in Europe.
They asked for a meeting with the French official to discuss concerns about the perceived threat to their legal rights as a result of the UK's decision to leave the EU.
There is continuing concern, particularly about the citizenship rights of EU citizens in the UK and also the estimated 1.5 million British citizens who live and work in European countries.
Among those meeting Barnier is Monique Hawkins, a Dutch woman who was told by the British Home Office to prepare to leave after 24 years living in Britain, many of them with her British husband and their two children.
But in a letter to campaigners, Barnier, a former European Commissioner, promised Europe was "committed to addressing their issue as a top priority in the upcoming negotiations" and that "our goal must and will be to create clarity as quickly as possible."
A letter sent by the French official's taskforce on the UK negotiations reminds the groups that there can be no negotiations before notification of article 50, which is due before the end of this month.
It also agrees with them that the protection of rights "must happen through an EU-wide process, and not bilaterally between EU countries and the UK."
A spokesperson for British in Europe, a coalition of 12 citizens groups in the EU, said, "We are pleased Michel Barnier wishes to engage with us, and will be asking him to seek a rapid solution based on maintaining the existing rights of four million people - including the three million EU citizens now resident in the UK - currently trapped in Brexit limbo."
Ahead of that meeting, which will be held in Brussels on 28 March, Barnier will this week join local civic leaders to discuss the impact of Brexit on Europe's regions and cities at a Committee of the Regions plenary on Wednesday and Thursday 22-23 March.
Also taking part in the Brussels debate on the future of Europe are MEPs Guy Verhofstadt, Parliament's Brexit negotiator, German EPP group member Elmar Brok and German Socialist MEP Jo Leinen.
The debate will take place shortly before the UK is expected to launch negotiations to leave the EU.
A CoR spokesperson said, "Barnier will discuss the implications of the UK's decision for cities and regions with members of the CoR."
The next day, local and regional authorities are to set out their position by voting on a Brexit resolution.
The CoR debate comes just two weeks after the British House of Commons rejected an amendment to the article 50 bill which sought to guarantee an early deal on the rights of EU citizens in the UK.