Do not search for "rtl8196e openwrt" hoping for a download link. Instead, search for "rtl8196e u-boot" or "rtl8196e SDK buildroot". Or simply recycle that old router and buy a device listed on the OpenWrt Table of Hardware .
If you're interested in exploring the possibilities of RTL8196E with OpenWRT, here are some steps to get you started: rtl8196e openwrt