Judging by EU timelines, the thirty-year gap Iger laid out would land us somewhere around "The Dark Nest Crisis" (a.k.a. The Killik Expansion). In that saga, a psychic insect race known as the Killiks had disputes with the Galactic Alliance and Jedi Order that led to the brutal conflict known as "The Swarm War".
The key things to note about this slice of EU, is that it features old players like Han Solo, Leia and Luke Skywalker, as well as pivotal points for their offspring. Jacen Solo (one half of Han and Leia's twin babies) returns to the Jedi after a long absence (with new Dark Side tendencies in his heart). In that same era, Jacen also becomes Jedi Master to Luke's son Ben Skywalker, a young boy who joins the Swarm War. Beyond that, this section of the EU continues to introduce and/or feature other elements of Star Wars lore that either have significance to the past films or subsequent EU stories.
The fimmakers behind Episode VII maintained early on that they wouldn't be beholden to the EU continuity, but lately rumors have pointed to EU characters indeed being mined for these new films. Based on the casting that is either confirmed, almost confirmed, or rumored to be happening, it's not hard to see the EU connections.
When Girls star Adam Driver was cast in a "villain role" I immediately immediately thought he was good for Jacen Solo's slow and painful turn to the Darkside; actors like Jesse Plemons (Breaking Bad) and Ed Speleers (Downton Abbey) are rumored for the lead actor shortlist, and fit the mold of Ben Skywalker (or Anakin Solo); before 2012 rounded out, it seemed like many young actresses were stepping up to audition for a role that could easily be Jaina Solo; and even recent casting news like Lupita Nyong'o being considered as a lead had me wondering about her playing Lumiya and/or Vergere, the female Sith Lords who convert Jacen Solo to the Dark Side.
It doesn't stop there: The Swarm War involves the Chiss, the alien race that the infamous Admiral Thrawn came from; with a bit of reordering, one could fold the "Thrawn Saga" into the other elements of the Swarm War storyline (and wouldn't Benedict Cumberbatch be a good Thrawn?). We could go further down this rabbit hole - Lando Calrissian and his YVH battle droids influencing the Swarm War, etc. - but I'll stop before we get too deep into nerd knowledge. Suffice to say: evidence of EU ties are piling up high. A year ago, I myself predicted Episode VII could adapt an EU storyline that soon follows The Swarm War so this evidence has been on the table for quite a while.
...And why not? The EU is considered lore by many hardcore Star Wars fans (often the harshest critics of the franchise) and even if the storylines aren't fit for film, the characters certainly are good inspirations for cinematic character arcs. It's also a built-in way to use Episode VII as a springboard, since the EU has a clear roadmap for transitioning focus from older characters like Luke, Leia and Han, to new characters like Jacen, Jaina and Ben. By Episode VIII, we could truly be on to new things.
With 30 years separating the Star Wars OT and this sequel trilogy, it will be interesting to see what this new era brings, EU-based or not.
Star Wars: Episode VII is scheduled to open in U.S. theaters on December 18th, 2015.