The first glimpe of the creatures' seemingly inevitable meeting was in 1990, at the time of Predator 2's release. Stan Winston's team crafted an Alien skull for the Predator's trophy rack at the end of the movie, as something of a wink at their previous work, Aliens. Although, contrary to what many may believe, this was not actually the original inspiration for AVP.
Dark Horse Comics were originally proposing some crossover work in the early '90s. One of their first ideas was to do a crossover between one of their own characters, Bizarro, with a character created by DC Comics entitled "The American". After considering the idea, they came to the conclusion that it wouldn't sell enough copies, so they started throwing other ideas around. Shortly afterwards, Editor/Artist of Dark Horse Comics, Chris Warner, conceived the idea of crossing over the two creatures while taking a bathroom break. The decision was unanimous, & it took only 15 minutes for Fox to give them the green-light to go with the idea. The series eventually went on to sell millions of copies, & at the time was the most successful non-Marvel or DC comic in history.
By 1994, ideas for making an AVP movie were already in the works, although we now know that they weren't followed-on until a decade later. Although during that large time span between conception & the movie's final release, the AVP phenomenon had spread into other categories, & had become well renowned in both videogames & in-depth novels.