As predicted, the car will share its rwd platform with the already-announced Genesis sedan, which we should see in about a year. The Tiburon replacement should show up half a year to a year after the sedan, and might even come as a convertible. In fact, there is also a suggestion that we'll be seeing several models based on this platform. We're not sure if the coupe will share the sedan's new V8 in addition to the expected V6, but it would make an interesting competitor for the Mustang if it did. Hyundai has officially said no, but there are still whispers, and if not a V8, some kind of boosted V6 in the top models might suffice.
[Source: Automotive News, sub. req.]