Can I claim the monthly HRA administrative fee as a medical deduction on my personal itemized tax return?

My retirement system has set up an HRA administered by a 3rd party.  The retirement system puts money into the HRA each month.  The 3rd party administrator charges a monthly fee.  Even though this is not an out-of-pocket expense for me, it does reduce the balance in the HRA that is available for me to use for medical reimbursements.