Kasich is one of 10 GOP governors who have embraced the Medicaid expansion over the objections of their party. The policy has strong opposition from Ohio's Republican legislature.
The Controlling Board has is made up of four Republicans, two Democrats and a chairman who was appointed by Kasich, according to the paper.
The Affordable Care Act allows states to expand Medicaid eligibility to people living at or below 133 percent of the poverty line using mostly federal dollars.
—This post was updated Monday at 10:15 a.m.