While there haven’t been any official announcements, recent activity within each franchise could indicate that a third Alien vs. Predator film would be possible after all these years. Alien vs Predator was released in 2004 when the two franchises were practically dead, and it spawned a sequel, Alien vs. Predator: Requiem. Even though both movies were poorly received by the audience and by the critics, they did okay financially (via The Numbers) and created an entire mythology that sort of exists as its canon within the Alien and Predator movies.
The Alien franchise and the Predator franchise are two of the most iconic sci-fi horror sagas ever. They have both spawned several films, including sequels, prequels, and crossovers. One thing these two franchises have in common is that they were born more than 30 years ago and, throughout that time, they’ve had their ups and downs, but they were never fully dead. Currently, the upcoming Alien and Predator projects seem to set the perfect landscape for another crossover to happen.