The childcare centre, along with Morley Library, is set to move out of the Galleria to make way for German discount supermarket Aldi.
Its lease was due to run out last week but the Galleria has given the community organisation a two-month reprieve.
The neighbourhood centre looks after 38 children, including 24 babies.
Bayswater Childcare Association chairman Mike Anderton said staff were already starting to pack for the move.
Construction is continuing on a new Derrick Ernst Neighbourhood Centre at the old West Morley Pre-Primary School site.
“The builder is eight days ahead of schedule so we’re looking at hopefully moving in to Tara Street around the second week of June,” Mr Anderton said.
“The Bassendean Men’s Shed is going to assist with the move.”
Mr Anderton said the new centre still had to pass Department of Education assessments.
Meanwhile at the same site, Morley Library closed on Thursday to move to the Les Hansman Community Centre. It will reopen on May 16 at the community centre.