Yes, there is a very good chance to get an upgrade with money.
Usually, Korean Air will calculate the difference between your original booking class (travel class Economy) and the current available booking class (travel class Business).
Depending on the fare rules of the original booking class, a change fee might be added.

My advise would be to buy the upgrade on the phone asap, because the availability of cheaper business class booking classes might be better today than at the time of check-in.