Arsenal executives are also questioning whether Wenger can topple the best clubs in Europe after their abject surrender against Bayern — the Gunners' seventh consecutive exit at the first knockout stage of the Champions League.
His future is more uncertain than ever following continued protests by unhappy supporters.
A source close to him told The Sun: “It is 50-50 now — I don't think Arsene expected to be beaten like that at the Emirates.
“Arsenal are his club and he wants to put everything right. But nobody knows whether he'll carry on after the end of the season."
Wenger responded to the defeat by giving his players the day off before they start preparations for Saturday's FA Cup home quarter-final against non-league Lincoln.