Rumors continue to persist that CBS is going to flip their Late Night hosts Could late night TV be seeing another major shuffle when it comes to the stars hosting the programs which dominate the later hours? After major shuffles in late night TV in the last two years which saw legendary hosts retire, and a number of others shuffle from different shows and networks, another move may be in the works according to a recent rumor, with Stephen Colbert, who left his Comedy Central show The Colbert Report in 2014 to replace David Letterman as the host of The Late Show in 2015, reportedly being switched with James Corden, the host of The Late Late Show.