In December, Parkhead chief executive Peter Lawwell gave his backing to the under-fire head coach in a video address to fans but promised “progress will be reviewed in the New Year”.
Results have failed to improve with Wednesday night’s 2-2 draw in Livingston leaving Celtic 20 points behind Rangers in the Scottish Premiership title race, and Lennon with just seven wins in his last 22 fixtures, and no wins in four since the turn of the year.
Irate fans have been demanding answers from the club on social media with supporter liaison officer John Paul Taylor facing questions on when the outcome of the 'review' will be made known.
In a reply to one fan, he tweeted: “As far as I’m aware it was planned to provide an update on the review in the next week or so.”
It comes as Lennon told Celtic they will have to sack him if they want a new boss after insisting he will not quit his Parkhead job.
After the 2-2 draw in Livingston, the Nothern Irishman said: "I won't walk away, absolutely not. I've put too much into this. Too much of my life.
"If the club have to make a decision then they have to make a decision. You're asking the wrong guy about my position.
"I'm fed up answering it really. Everyone is interested in my job. You keep asking if I'm going to be here. I will be until I'm told otherwise.”