The charity says the site is outdated and unsuitable for redevelopment.
The Blue Cross chief executive Kim Hamilton said: “Our charitable funds are becoming increasingly stretched, especially in the current financial climate, while animal welfare issues across the country are changing.
“The proposals we are discussing with staff aim to help more vulnerable animals and owners nationwide by focusing our limited resources in areas where we can achieve more.”
Over the last six months, The Blue Cross has undertaken a widespread review of animal welfare needs and its ability to meet those needs through its network of animal adoption centres, equine centres and animal hospitals nationwide.
Extensive research conducted by the charity identified that animal welfare issues in some areas of the country, such as the North West, are not being sufficiently addressed.
Twenty-seven horses currently live at Northiam and would be relocated to the other equine centres if the move is approved.
In 2009 The Blue Cross carried out more than 100,000 veterinary consultations and procedures for the pets of owners on low incomes and found homes for over 6,000 unwanted and abandoned dogs, cats, horses and other pets.