Unfortunately this is not possible, Application Gateway does not have a way to alter outbound traffic on members on the backend pool. Azure Load Balancer can, and you can view more information about outbound connections with a VM Here. That doc mainly refers to Load Balancers, but describes how VMs send outbound requests as well.
The easiest way to control the IP that your VMs send requests from is to use a Public IP on the VM, or you can use Azure Virtual Network NAT to consolidate outbound connections inside your Virtual Network.