While it's not something you'd usually associate with the likes of FIFA or Madden, 2K Sports NBA series does have a MyPlayer mode and EA may be looking to follow suit.
The Narrative Designer jobs are described as follows:
"The Narrative Designer will bring the player’s experience to explosive life in its story-telling mode, championing story to the team and ensuring that script, speech and story-telling devices are tuned to achieve a gripping emotional narrative experience.
"You will create characters that game players fully embrace and bond to, and will capture emotional experiences that drive the story forward through non-linear storytelling techniques.
"You’ll work closely with other designers and producers to create game worlds where story is core to the player experience and will drive an innovative story vision that is central to one of EA’s AAA titles."
Of course, this isn't confirmation that FIFA 16 or Madden 2016 will have a story mode, EA may be planning to take their career and franchise modes in different direction. We're sure to find out more when those games are officially announced.
FIFA 16 has been in development since at least August 2014 so it may be something quite special this year.