Ohio Gov. John Kasich, who failed to make a mark in the 2016 GOP primaries, said it was "very unlikely" that he would run for president in 2020 - but he didn't rule it out. John Kasich won't rule out 2020 presidential run Ohio Gov. John Kasich, who failed to make a mark in the 2016 GOP primaries, said it was "very unlikely" that he would run for president in 2020 - but he didn't rule it out.