Motsoaledi revealed this in a written response to a question from DA MP Christopher Roos, who asked about the date for the re-opening.
Roos wanted to know what lay behind the delays that resulted in Home Affairs missing the March 2018 court deadline to reopen the centre.
He also asked about interim measures put in place to allow new asylum- seekers arriving in Cape Town to file their applications.
In his written reply, Motsoaledi said the date for the re-opening of the refugee reception office depended on the finalisation of the lease agreement with the prospective landlord and the refurbishment of the offices.
“The Department of Public Works and Department of Home Affairs have signed the lease contract, awaiting the same concurrence with the prospective landlord,” he said.
Motsoaledi said the procurement requirements of the Department of Public Works in acquiring office accommodation contributed to the delay in meeting the deadline.
The minister said only refugee applicants who were dependents of existing clients were allowed to apply in Cape Town.
“The rest of new applicants are encouraged to apply as they enter the Republic in refugee offices closer to northern ports of entry as most applicants enter through those ports,” Motsoaledi said.
In 2012, the department suspended the services to first-time applicants in Cape Town and Port Elizabeth - two of the country’s five offices.
Its decision was appealed in the Supreme Court of Appeal, which ordered the department to re-open the Cape Town Refugee Reception centre in 2017. The department appealed to the Constitutional Court, but the matter was dismissed.