Thompson tells The Associated Press he plans to file as a candidate Monday and launch his campaign Wednesday. He has represented Lakeville in the state Senate since 2011.
Thompson is an attorney and former talk radio host. He is a favorite of fiscal conservative and tea party activists.
Hennepin County Commissioner Jeff Johnson and businessman Scott Honour are also running. Former House Speaker Kurt Zellers is talking about his plans to consider running for governor. The incumbent is Democratic Governor Mark Dayton.