One politician already said he's exploring a run. : Republican Tennessee Sen. Lamar Alexander announced Monday he will not run for re-election in 2020, clearing the way for a number of competitors to chase after his open seat. Potential candidates whose names are already being floated include Republican Gov. Bill Haslam, Republican Rep. Diane Black and Democratic Chattanooga Mayor Andy Berke, reported USA Today. Republican Rep. David Kustoff’s office already said he is exploring the possibility of running, reported The Tennessean.