Bodies are already being stored at an unfinished mortuary as facilities reach capacity amid growing numbers of coronavirus-related deaths.
Work started on a temporary morgue at Birmingham Airport, where up to 1,500 bodies can be stored, on 27 March.
West Midlands Police confirmed part of the facility had been completed and was already being used for storage.
The temporary mortuary is due to be completed by 17 April "at the latest," the force said.
"It is anticipated that the site will be able to accommodate the number of deaths expected in the region, although our hope is that this will not be needed," the force said.
Police urged bereaved families "not to delay in making funeral arrangements" to prevent "prolonged storage".
A spokesperson for the force said police were working "to ensure that we deal with all deaths in a compassionate manner".
There were 113 deaths linked to coronavirus in the West Midlands on Tuesday, taking the total in the region to 912.
The emergency hospital site will initially have a 500-bed capacity for coronavirus patients which can be scaled up to about 1,500 or more if needed.
West Midlands Police said that while regional mortuaries were "reaching capacity", many burial sites and crematoriums were continuing services over the bank holiday to ease pressures.
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