The original NSX competed principally in Japan's own Super GT series. So did the subsequent HSV-010 GT that was originally designed to be the NSX's replacement. But Acura's new supercar is as much an American vehicle as a Japanese one, and as such it looks more likely to compete on American soil.
The options which Honda is considering boil down to GTE and GT3. What's the difference, you ask? Until just a few years ago, international sports car racing was split between GT1, GT2, GT3, and (to a lesser extent) GT4 classes. GT1 was phased out in 2009, GT2 was reformatted into GTE (with both Pro and Am categories), while both GT3 and GT4 carried on. Today GTE is run at the 24 Hours of Le Mans and its associated championships around the globe: the FIA World Endurance Championship, the European Le Mans Series, the Asian Le Mans Series, and the United SportsCar Championship. Meanwhile GT3 is run in series like the Blancpain Endurance Series and a growing number of regional championships. (GT4 is run in lower-level series for amateur racers.)
Acura currently runs the TLX-GT in the Pirelli World Challenge here in America. But as the series moves to GT3 specifications as well, the company is facing the decision of either adapting the existing racer to the new regulations (and coming away with a potentially compromised package), or replace it entirely. The NSX could prove just the ticket, however the GTE class may ultimately give it more exposure.
Whichever rulebook Acura opts to play by, it likely won't be running under hybrid power – an element which would add complication but not necessarily much benefit under current regulations. The automaker will also have to decide who will develop the new NSX racer, with both California-based Honda Performance Development (HPD) and Italian outfit JAS Motorsport (which fields Honda's WTCC team) eyed as potential candidates.