Norway rats are quite easy to litter train. I use super pet litter balls and place a pan in a low traffic corner. Place all poos in the litter pan and keep the rest of the cage spotless, let the litter pan get a little rank though.
First though, you will need to change their main bedding to fleece or something else. They need to understand their main bedding is not the texture to go to the bathroom on, but that the litter in the pan is what they are supposed to use.
Example: Main "sleeping" bedding is fleece, litter box contains super pet litter balls with a sprinkle of aspen/pine. They are used to defecating on the aspen/pine, so it will make things easier.
Males will mark with their urine, but most of their business (besides marking and the occasional accidents) will go into the litter pan. I have litter trained probably a hundred rats doing this. Usually they take two or so weeks. I have only had a few that refused to completely litter train.