It really depends how you look at it.
He STAYS, because...
1 - Leicester are a perfectly balanced squad punching above their weight.
2 - Leicester are nailed on top four, and playing like at least the second best team in the country.
3 - Leicester will offer CL football next season, which Arsenal will not.
4 - Leicester have solid foundations, and an upward trajectory.
5 - If you combined the two teams, perhaps 9 or 10 would come from Leicester currently, with only Auba guaranteed to start from the Arsenal side.
6 - He has only just got to Leicester, and needs to play a longer game.
7 - Better jobs than Arsenal could become available if he proves himself with Leicester.
He GOES, because...
1 - Arsenal will always be a bigger club than Leicester, no matter how tenaciously the Foxes overachieve.
2 - Leicester will not win the league, so he will probably not be giving up silverware.
3 - Arsenal are at their all time lowest ebb, so he will be given time and patience, and be at a club where managers can stay long term with even a modicum of success.
4 - No matter how well Leicester are doing, Arsenal's ceiling is much higher, as in CL every year, and perhaps competing for the league every year.
5 - Arsenal will pay him more.
6 - He will be able to build a squad in his image from the ground up at Arsenal, and receive all the credit for any success.
7 - Leicester is a stepping stone eventually anyway, and there are never any guarantees another big offer comes along.
Emotion would make fans believe only one of these lists could be true, but in reality, both are true, though I would argue the list for staying is still more powerful, I am just illustrating that it would not be insane for him to go. Either way, this would all depend on Arsenal actually offering him the job, and I suspect they will not, but will go for an Arteta or Ancelotti instead, who I can imagine appealing to their decision makers more.
For the record, I think Brendan would suit Arsenal very well. But I hope he stays at Leicester.