The £310 million loan on the site, home to the multi-storey Nike Town and TopShop outlets, is reportedly due for repayment in December.
Green is said to be talking with US specialist lender Apollo.
The existing mortgage was completed in 2014 by a Royal Bank of Scotland-led syndicate, and the property is estimated to be worth £400m.
The newspaper reported a source close to Arcadia claiming any new mortgage offer would be at a reasonable rate owing to the building’s saleability.
However, any refinancing will be complicated by Arcadia’s pension fund having been given a security over the building in a company voluntary arrangement (CVA) of June 2019 designed to prevent the group from collapsing.
Arcadia struggled to secure backing from landlords for the CVA owing to the size of rent cuts proposed.
The Green family eventually stumped up an additional £9.5m to decrease the percentage of rent reductions.
The CVA provided for closure of between 23 and 50 stores and rents cuts on almost 200 properties.