I don't think he will, and I don't think he should.
Let him lead Arsenal to yet another top-4 finish and then remind the fans of that, rather than leaving on a low point.
Since he's been manager, Man City have been relegated to the third tier and come back up, and every other 'big' club has shat the bed at least once and had a catastrophic season - Spurs had Tim Sherwood in charge FFS. A few years into Wenger's reign, Leeds United were Champions league semi-finalists.
Granted Arsenal haven't come close to winning the CL or the league in recent years, and I can see why the fans are getting restless, but the consistency at Arsenal is unbelievable. Even if it is consistently just below expectations, that's better than the odd spectacular failure everyone else has had.