The quest start is bugged. If you leave town or fast travel to it via COC the Jarl doesn't have the Topic to start this quest. No amount of resetting/starting/setstage the quest or the NPC or the cell fixes it. Some suggested that it is related to starting the College of Winterhold First Lessons quest but it isn't. I tested with First Lessons active and it works as long as the PC doesn't leave town. Addtopic doesn't work and fooling around with Factions doesn't change anything.

I know its not a critical quest but for OCD completionists its annoying and I'd rather not have to go to an earlier save and lose a tonne of progress.

Any help would be appreciated. Thanks.

This is a radiant quest, therefore, it may not start due to you having one or more http://www.uesp.net/wiki/Skyrim:Radiant#Quest_Locations active already. Completing any active radiant quests may fix this problem.

From the UESP wiki: If starting the quest via console does not work. You can bypass this quest and still become Thane of Winterhold on PC with setrelationshiprank 1c1b5 2 .