Staff at the shops in Cascades Shopping Centre and Fareham Shopping Centre, off West Street, are among 11,000 jobs being threatened.
A spokesman for the retailer said the 88-year-old business will call in administrators after being unable to secure a rescue package to save the firm.
Shopworkers’ trade union Usdaw said it was ‘seeking urgent clarification from the company.’
The collapse of BHS would be the biggest retail failure since Woolworths folded in 2008 with the loss of almost 30,000 jobs.