It's likely that the F35 wont reach export for 9 years.
I think they will try and build likely looking for a partner nation best bet being Turkey Who are also said too be looking into a new fighter program of indigenous origins along side the F35 although the turks and Koreans might have some issues too hammer out.
The Advantages of building your own are that you have total control of what you want in that craft, can deploy it with out need of assistance. and the Korean's have been wanting too build there own national defense industry for both the profit margins, the national pride and of course the fact that via building there own they don't need too worry about striped out tech. I feel that this will at the very least reach prototype but Korea will make it's own call. Turkey seems the best candidate due too it's own TfX program the close relations they have in two other military programs. Including main battle tanks and IFV's