Working without SNAT to see original client IP

You'll need to create a forwarding virtual server on the BIG-IP to enable routing to that network through the BIG-IP. Basically just a Virtual Server with a destination of 0.0.0.0/0 and type of Forwarding (IP) for the pool member to use and one for the network to access the pool member with a destination of the pool member's network, i.e. 192.168.10.0/24. On your network, you can set a route to the network the F5 is routing by adding a route with a next hop of the BIG-IP's floating IP.

Here's a KB explaining forwarding virtual servers:

https://support.f5.com/csp/article/K7595

--D