Liverpool City Council want to encourage residents to get to know their neighbours to "create stronger communities".
People are being asked to arrange events including coffee mornings, picnics, or street parties.
Councillor Marilyn Fielding said good neighbour relations "is an important part of making our communities a safer, happier place to live".
The idea is part of the city's take on European Neighbours Day.
"The week is a great opportunity for people to get to know their fellow residents and celebrate the importance of community life," Councillor Fielding said.
Events should be registered with the city council, which will help promote them.
The official day is Tuesday 26 May and more than eight million people are expected to take part across Europe.