Maybe, but probably not on planet Wenger.
If he can win the FA cup after an unbeaten run in our next 7 league games, possibly with a big performance against Spurs and/or United then he'll probably convince himself that we've turned a corner and he's still got it.
And winning the FA cup before has been on the whole an unspectacular achievement. We beat a shit Hull and a dogshit Villa in the finals, we blagged our way past United with what was effectively an own goal. If he was to win this one then he'll have toppled Guardiola in the semis and beaten a solid Chelsea side who will probably be league champions at the time in the final. That would show this side had some bottle and again probably convince him that we'd turned a corner and next season will be great.
I think the only compromise I could take with him staying is him signing a one year deal. It seems fair after he's basically shown that he's past it now and if he won't ever resign mid-contract then it'll be the tidiest way for him to get out when the time comes and also mean he has something to play for.