The Chicago Democrat says that would be the wrong way to go.
All but one of the seven Republicans running for governor say they would reject a government-run health plan. A provision to let states opt out is being considered in Washington.
Quinn also said Friday that he disagrees with Republican Jim Ryan's call to lower the minimum wage in Illinois by 75 cents. Ryan says that would help make Illinois more competitive economically.
Quinn made his comments at an event where he picked up several endorsements, including one from Chicago alderman Dick Mell, the father-in-law of ousted Gov. Rod Blagojevich.