I'm going to be blunt. I don't think FD just hands licences to anyone. Are you an established & published author? Because if not I wouldn't get your hopes up.
That might sound a bit harsh.
My suggestions would be: If you don't have experiences with writing books, then just start and DO IT!
You will soon feel whether writing a story in the ED universe is really your cup of tea, or if it just has been a quick idea. You will have had your fun and enjoyed it in any case, and that's what is most important. So: Don't actually worry about licenses until you know that that step will be necessary. First of all, enjoy writing!
Oh and there is always the option to write good solid sci fi outside ED, even if it is basically close to and inspired by ED.
And if you really feel the need to get a permission in advance, why not contact Frontier support by labelling it "Fan Fiction", and ask them about Do's and Don'ts. An official book is one thing, Fan Diction like those published in magazines or for free is quite another matter.
But most important: Get your pen / keyboard, switch on the music LOUD and WRITE AWAY!!
(and yes, I am a writer by profession).