"We're definitely talking about the next one, but we haven't talked about a release date," Burk told Digital Spy. "We don't want to wait four years, the same amount of time between the last one and this one, but [2016] is going to be a big year to celebrate hopefully."
At this point in time, it's unclear whether Abrams will return to direct the next Star Trek movie, given his commitments to Disney's Star Wars: Episode VII - which is expected to arrive in 2015 - although it is thought he will continue his involvement in a producing capacity at the very least.
Star Trek Into Darkness is set to arrive on May 9th in the UK and May 17th in North America, with a cast that includes Chris Pine (This Means War), Zachary Quinto (American Horror Story), Zoe Saldana (Avatar), Karl Urban (Dredd), Simon Pegg (The World's End), John Cho (American Reunion), Anton Yelchin (Fright Night), Bruce Greenwood (Flight), Benedict Cumberbatch (Sherlock), Alice Eve (Men in Black 3) and Peter Weller (RoboCop).