BIG IP as a load balancer for service discovery

Okay, I think I understand. BigIP is a full proxy system. The legacy app would make a request to the IP and port of a virtual server on the BigIP. If you have different back end IPs depending on the URI, then yes, the BigIP would need to look at the URI. It can do this by adding an HTTP profile and either configuring a local traffic policy or an irule. The fact that it's a REST call shouldn't be relevant. So here is how it would work.

Your client would send a request to the Virtual server which would terminate SSL (if needed) and inspect the HTTP payload of the TCP packet. Based on the rules you had defined it would then pick a pool member (back end server) to send the request too. The fact that it's a REST call is only as relevant as you would like to make it.

You can read about local traffic policies (the easiest, and least flexible way) here: https://support.f5.com/csp/article/K04597703

If you would like to use irules instead (the most complicated, and most powerful way). A devCentral search for URI load balancing or URI redirection should return many examples, but here are two that may be relevant to what you want to do:

https://devcentral.f5.com/questions/help-with-irules-and-uri-redirection-54035

https://devcentral.f5.com/questions/http-header-and-uri-redirect

In your case I suspect the first example will be more helpful.

Note that the next two days are the Thanksgiving holiday in the US, so responses may be delayed.