You can give them some newspaper or butcher paper and see what they do with it. Some will have no interest at all in tearing things up to nest with while others will go nuts with it. My boys in particular like to shred paper whereas my girls would rather drag around small pieces of fleece to bed down in. I like giving my rats different materials in their cage just to keep them occupied during the day (paper, fleece, aspen, empty toilet paper/paper towel rolls, etc.). Rats really aren't picky about what they play with or nest with, so common items that you'd normally just throw away (like the empty toilet paper rolls) can be used as toys
My rats love to pull the fabric off the shelves to make HUGE nests, so yes, many rats will love to make ugly nests
I usally give mine lots of paper towels, pieces of fabrics, old shirts, toilet paper rolls, tiny cardboard boxes and pretty much everything that isn't harmful and that would anyway go to waste. I even take pieces of fabric and tie them to the sides of the cages so my girl Sake can chew them off and use them as nesting material, it keeps her occupied a lot of time and she seems to love chewing those things and drag them to her nest.
My one girl LOVES to nest. I cut up old rags into strips for her and place them by her food bowl. Then I watch her pick them up one piece at a time and run to her shelter in pure joy! However, they don't need it. But it is incredibly enjoyed. There is no reason to get fancy about it. You can use things that you would throw out anyways, EXCEPT anything that may suffocate them! No plastic bags and wrappers. Cardboard and fabric are favorites!