The Green Brigade have voiced their opposition to those running Celtic.
The influential supporters group say urgent change is required both in the Parkhead boardroom and the dugout.
The position of manager Neil Lennon has come under intense scrutiny, with the club having won just two of their last eleven games in all competitions.
Ugly protests outside Celtic Park followed the Hoops' 2-0 defeat to Ross County in the Scottish League Cup second round.
But the Green Brigade have now turned their focus on the club's largest shareholder - Dermot Desmond - and chief executive Peter Lawwell.
"Whilst we still believe that a managerial change is unfortunately necessary, the structural problems within the club run deeper," a Green Brigade statement said.
They feel there is "a growing disconnect between those who run the club and those who sustain it - epitomised by todays pictures of fencing around Celtic Park to keep fans at bay."
Celtic go into Sunday's meeting with St. Johnstone 11-points adrift of leaders Rangers as they continue their quest to win ten Scottish Premiership titles in a row.
The Green Brigade are calling for "leadership that puts the good of the club first".
They add, "If the current custodians cannot provide that in this crucial moment, they are demonstrating that they are unfit to hold the positions that they do."
Green Brigade statement:
Events over the course of the last two weeks have further highlighted that change is desperately required at Celtic Football Club.
Three consecutive defeats have added to an already disastrous start to the season.
Developments off the park have been equally troubling as the Celtic board appears woefully unprepared to make the change required, whilst briefing journalists that they are set on retaining the manager to spite fans who have sought his removal.
There is a growing disconnect between those who run the club and those who sustain it - epitomised by todays pictures of fencing around Celtic Park to keep fans at bay.
In a year when fans have been asked to pay full price for a season ticket for matches they cannot attend, amidst a global pandemic and economic recession, a clear message by the has been sent to the Celtic support millionaires in charge of our club - that we do not matter to them.
Our passion is only acceptable if it can be commodified, our support only truly important when season book renewals are issued.
Whilst we still believe that a managerial change is unfortunately necessary, the structural problems within the club run deeper.
A boardroom dominated by an absentee landlord major shareholder who puts his own ego above the interests of our club in this most historic of seasons.
A Chief Executive paid £3.5m last year, with no contingency plan for our season and who bears primary responsibility for the situation we now find ourselves in.
A recent statement released in Peter Lawwell's name urged unity, but this can only occur with leadership that puts the good of the club first.
If the current custodians cannot provide that in this crucial moment, they are demonstrating that they are unfit to hold the positions that they do.
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