Manager Martin O'Neill says he'll ‘genuinely reflect and see’ over the international break whether he feels he can come back and turn things around at Celtic.
His side were beaten 1-0 by Rangers at Parkhead this afternoon with Ryan Naderi's first-half strike proving crucial.
It was Celtic's second defeat to their great rivals in eight days, and third loss on the bounce.
"I genuinely will reflect and see," O'Neill said of his future. "It's a matter of whether I can help the team. That's the manager who's supposed to be able to do that. I will have a look at that this week.
"I think that every single time that something crops up, things don't go so well, age plays a part. And you know what? They may well be right.
"I'll obviously speak to the board. And you never know, they may want to speak to me."
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Sunday's result moved Rangers within just two points of Celtic at the top of the William Hill Premiership table. While O'Neill's side still lead the way seven matches into the new season, he understands fan frustration.
"I'm not immune from criticism. Far from it. Absolutely and utterly far from it," he added. "I think there's every reason to ask, can you turn this round? Can you change the whole thing?
"We are two points clear, so I have to kind of look at the bigger picture at this minute. But I knew that we were in a big, big fight anyway, with both ourselves, Rangers, and Hearts again, who are far from out of anything.
"It's a long season ahead. It's not the first time I've been questioned about my managerial time. So, yeah, I'll have a look at it. I will reflect and see."