Can an incumbent governor from LA, MS or KY ever become president?

[solarstorm]

In order to get the nomination by their party, a presidential candidate has to go through hell a long primary process, which they have to prepare for in the year before the presidential election by traveling throughout the whole country, especially to Iowa and New Hampshire.
We all know that Louisiana, Mississippi and Kentucky hold their governor races one year before the presidential election. At the same time, an incumbent governor from one of those three states who wants to run for president has to campaign in their own state. A loss in the gubernatorial race would render any hopes for the highest office void, thus they have to campaign very hard in their home state, which leaves no time and resources for canvassing in other parts of the nation.
And bear in mind, they have to govern a state during the primary process.
Is it even possible to campaign for those two offices simultaneously? Or does such a governor have to wait until the end of his tenure?

[solarstorm]

I've changed the title to "can" to make the purpose of the question a bit more clearer.