The affected stores employ 930 staff, Deloitte said. Last week, it was confirmed that about 190 jobs had been shed across HMV's head office and distribution network.
HMV entered administration in January.
It has faced intense competition from online retailers, digital downloads and supermarkets in recent years.
HMV currently operates from 220 stores in the UK.
Deloitte said no fixed date had been set for the closure of the 66 identified stores, which would continue to trade in the meantime.
"This step has been taken in order to enhance the prospects of securing the business' future as a going concern," Nick Edwards, joint administrator at Deloitte, said.
"We continue to receive strong support from staff and are extremely grateful to them for their commitment during an understandably difficult period.  All other key stakeholders remain very supportive and I continue to be hopeful of securing a future for the restructured business."
The stores earmarked for closure are:
The administrators have been in talks with restructuring specialist Hilco about taking over HMV.
Hilco, which already owns HMV Canada, has bought HMV's debt from its lenders, a move that could pave the way to taking full control of the company.
The administrators of HMV have said that 66 of the music and DVD retailer's stores will close over the next two months.