Red, white and black work well together to make a graphic combination. If you use a black rug, it will ground the sofa without diminishing the sofa's impact. If you go further and pair the rug with espresso colored tables, metal accent pieces over an espresso hardwood floor, then your composition will appear more unified with the black and espresso pieces acting as a neutral backdrop for the diva sofa. This combination is often easy to achieve.
A white rug will soften the impact of a red-and-white couch. Be careful to select a crisp white, or the red of the couch will make an off-white rug look pink or dirty. White is a neutral and it allows you to bring in other colors, woods, metals, plastics or upholstery. Because red is a saturated color, you will usually not want to bring in other red pieces that may be a slightly different color than the couch.
To transform the red into a neutral, consider going with a red rug. If the rug is red and the drapes are red and there is a solid red chair, the impact of the couch is reduced by each additional red item. This allows you to use white or black as an accent color and to bring in stripes or other bold patterns. This type of room has a lot of color, which may make it feel a bit aggressive.
Take a look at the red and the white individually. Is the red a pure red or close to burgundy? Is the white a crisp white or antique white? Often a rug can be paired with a couch if the rug and couch share the same colors, even if the rug has more and different colors from the couch. If they have the same colors in common, usually you can bring them together successfully. It is likely more detailed rugs will change how the colors of the couch look, because furniture picks up surrounding colors. Try out rugs before you buy them to make sure you achieve the look you want.