This can be done if your router supports configuring DHCP option 121 - The Classless Static Route Option.
Judging by the user guide, your router does not support this, so you're probably looking at getting an enterprise-level router, or flashing your current router with custom firmware that supports setting this DHCP option (such as DD-WRT).
Alternatively, you could look into installing a DHCP server on your Linux distribution and setting it up to distribute this option to clients along with their IP configuration. Remember to disable the DHCP server on the router so that only the DHCP server running on the Linux distribution will receive/reply to DHCP requests. Assign the machine a static IP configuration (IP address, subnet mask, and default gateway), and make sure the chosen IP address is outside of the DHCP scope and you should be good to go.