Ex-Arsenal defender Lee Dixon said: "This team is getting no response from him. I've never seen him like that."
Frenchman Wenger, at the helm since 1996 but whose contract expires at the end of this season, has not won the Premier League since 2004, but Keown told BT Sport: "Arsene must be considering his future now."
Former England full-back Dixon added on ITV: "He just seems so low.
"That is the first time where I've seen him where I've thought, 'he thinks it's time'. The fact that he hasn't been able to get a response from the players in the last few weeks might be the final straw."
Arjen Robben fired German champions Bayern into the lead at the Allianz Arena on Wednesday, but Arsenal fought back and equalised when Alexis Sanchez followed up and finished his own saved penalty.
However, in the second half the Gunners capitulated, as Bayern excelled in a 10-minute period during which Robert Lewandowski restored Bayern's lead before Thiago Alcantara scored twice.
Substitute Thomas Muller scored late on to surely put the tie beyond the Gunners.
Keown - a defender who made 449 appearances for Arsenal - said recently he expected his former manager to get one more season. However, after watching the Bayern defeat as a pundit for BT Sport, Keown questioned whether he should stay.
"It's almost embarrassing. Outclassed, outplayed," he said. "I can't ever say I'd like to see him go (but) this is his lowest point ever as Arsenal manager."
Last week, former striker Ian Wright, who scored 185 goals for the Gunners from 1991-98, told BBC Radio 5 live he did not expect Wenger to stay on next season.
After the drubbing in Germany, Wright posted his frustrations on social media and declared he was "not watching anymore".
Bob Wilson, goalkeeper in the first Arsenal side to win the double in 1971, told BBC Radio 5 live on Thursday: "I wouldn't be at all surprised that Arsene now, with the amount of headlines that are coming his way, will look at that and say 'two decades'.
"He might just look at that and say 'OK enough is enough' because I think as a human being you can only take so much.
"He's a very sensitive guy and he's hurt, I doubt he will sleep very much between now and a horrible game on an artificial pitch at Sutton."
Arsenal's next fixture is an FA Cup fifth-round tie at non-league Sutton United on Monday (19:55 GMT kick-off).
Reaction to the Bayern beating
Arsenal's only major silverware in recent years has been consecutive FA Cups in 2014 and 2015.
Successive defeats by Watford and Chelsea dented their league campaign, and although Wenger's side returned to winning ways with a 2-0 victory over Hull last weekend, the Gunners are fourth in the table, 10 points behind leaders Chelsea.
Former Chelsea winger Pat Nevin was at the Allianz Arena for BBC Radio 5 live and described Arsenal's performance as "shambolic".
"The negativity before the game feels more like a realism," he said. "Arsenal were totally outplayed by a team who are good but weren't utterly brilliant.