Disgruntlement among the Celtic support intensified after they drew 1-1 with St Johnstone on Sunday to leave them 13 points behind Scottish Premiership leaders Rangers with two games in hand.
But the Celtic board released a statement making clear its “continuing support for Neil and his backroom team”, who are chasing a record 10th title in a row.
“The board recognises and understands the importance of winning the league championship this season,” the club said.
The statement added: “Whilst it has been suggested that it is time for a change, at this stage in the season the board believes that Neil and his management team are best placed to turn the team’s performances around and lead us on to success.
“The board continues to work closely with Neil and his team to support them as they seek to do so and progress will be reviewed in the New Year.”
The Hoops have not won in five matches and have only recorded two victories in 12 games.
A home defeat by Ross County in the League Cup last week sparked angry scenes outside Celtic Park, with police reporting three injuries for their officers. The club said players were left “shaken” after being targeted by missiles.
Celtic chief executive Peter Lawwell called for “strength in adversity” as fans demanded the sacking of Lennon.
After defeat by AC Milan and more dropped Premiership points, there were more protests on Sunday amid a heavy police presence, with footage showing fans running after the team buses to express their displeasure.
But the club’s power-brokers have stood by Lennon, who can clinch last season’s treble on December 20 when Celtic face Hearts in the delayed Scottish Cup final.