Another way this could be implemented would be like the records of eminence quests (storyline, not goals). When you enter a zone and meet the requirements for the starter quest as well as after you've completed 50 of them (and I assume 100) you see a short message to the extent of "You have an inclination you should speak with [NPC Name] around [Position]".
If you have a lot of quests flagged this could spam your chat log so a little text command to enable/disable it would be great. I don't know if other people are like me, but I'll get into "quest mode" where all I'll want to do are quests for a day or week, and then I'll decide to focus on battle content for a while, so enabling/disabling this would be great.
This would resemble the recommendations feature of XIV more than the floating quest icons.