Just to be clear, I have no idea whether Arsene Wenger plans to stick around as manager of Arsenal next year. In fact, I've been told that he has not decided yet and it will depend on how things pan out. (Others say his decision was made a while back, which only goes to show that very few really know.)
What folks who know him fairly well have told me, however -- and, I think, is more than plausible -- is that he is far more likely to leave on a high than on a low. In other words, had Arsenal's season petered out with a sixth-place finish (which is exactly where they were after the derby defeat to Tottenham Hotspur) and humiliation in the FA Cup final, then he would have wanted to stick around to "fix it." But if the season ends on a high, either with that "fourth-place trophy" (sorry, couldn't resist) or the FA Cup (or both), then he might be more open to calling it a day.
Saturday's 4-1 hammering of Stoke City made it three wins on the trot for Arsenal. They have two more home games against beatable opponents (Sunderland and Everton) and then that Wembley Stadium date against Chelsea. There's every chance they'll finish on a high and we'll get to find out if that theory was accurate or not.