Yes it is possible. You only have to highlight the net and the rat will take on the colour you use. Also a good idea is to have solid hilight on instead of zebra highlight, the ratnest has a zero line width and the highlight may not show up properly on zebra.
The highlight solid or striped is a user preference setting.
we have it so we can change it using the functions keys (this is set in the pcb env file).
However you can find the setting by going to setup/user preferences and going to the display folder then go to the preference 'display_nohilitefont' if it is ticked then the highlight should be solid unticked and it will be striped.