If it's monitor requests, the traffic will be sourced from the Linux host and not use a virtual server. Or are you trying to poll the new router through LTM from another host? If the former, you should be able to just configure a route for the router pointing out the correct VLAN. For load balanced connections, you could create the same route and then create a forwarding virtual server on the same IP address as the router with no iRule. By default with such a VS, LTM will not answer ARP for the IP, but will accept traffic for that IP and forward it according to the routing table.
Aaron