There are many animal sanctuaries that you can visit and have a close or one-on-one interaction with wild animals especially in Kenya. Many if not all sanctuaries are purposely started to help orphaned, endangered or very young wild animals to get on their feet before being released back to the wild.
Ol Jogi Private Wildlife Conservancy
Lewa Wildlife Conservancy
Ol Pejeta Conservancy
The David Sheldrick Wildlife Trust