It seems inevitable that a LEGO game based on Star Wars: The Force Awakens would be coming. Not only has there been several leaks by chains, but a reveal trailer has been found, too.
For starters, an Amazon Italy page not only listed the game but also the plot, before it was taken down. According to the product page, "the game also will contain exclusive playable content that bridges the gap between the story of Star Wars VI: Return of the Jedi and Star Wars: The Force Awakening." This makes sense because the previous LEGO Star Wars titles have included multiple films in each game. It also wouldn't even be the first game to add a bridge between The Force Awakens and the original trilogy; Star Wars: Battlefront featured The Battle of Jakku content.
Furthermore, both Xbox.com and some other listings erroneously posted the game's teaser and other info such as a 28th June release date. Although the trailer was taken down, a gaming site managed to rip the teaser before it was removed. The teaser itself is a parody of the original teaser that was unveiled back in November 2014.
UPDATE: Warner Bros. Interactive has officially announced LEGO Star Wars: The Force Awakens, with a confirmed 28 June 2016 release date.
According to the press release: "Launching on June 28, 2016, the game will introduce brand new gameplay mechanics to build, battle and fly through the galaxy like never before, as well as new story content exploring the time between Star Wars: Return of the Jedi and Star Wars: The Force Awakens, providing additional insight about the new movie and its characters."
LEGO Star Wars: The Force Awakens will include some new features such as Blaster Battles, which uses the game environment to drive back the First Order, as well as arena-based space battles and dogfights using various ships including the Millennium Falcon. The Multi-Builds system allows players to choose from multiple building options to advance the single player game.