Despite not being the same runaway success as the remake of Resident Evil 2, Resident Evil 3 has still become a fairly big success for Capcom with more than two million games sold in April. However, this doesn't mean that there will be any DLC made for the game. In an interview with Siliconera, producer Peter Fabiano says it is simply a "finished product":
Resident Evil 2 got a couple of minor DLC updates, but the third game clearly won't. It's worth pointing out, however, that this does not apply to Resident Evil: Resistance, which likely will be fleshed out as long as people play it.