Though it's not an official thing, I like to think all the FF worlds are connected together through Atomos, since he's essentially a gateway to all time and space and has shown up in multiple games.
If you really want to link the games together, just do what I did; My character from FF11 was using Atomos until one day something went wrong and I got barfed up in Eorzea (Atomos was showing up just before Dalamud fell). That's the basic backstory to my character in FF14. Done and done, right?
Although, I still play FF11 on occasion so I like to pretend it happens in the "future", heh.