The Celtic Trust say the club's board have knocked back their share proposal.
The Trust had drawn up a plan which asked the club's hierarchy to consider offering shares to supporters who bought season tickets last season.
The move comes after fans were been locked out of Celtic Park in the midst of the Covid pandemic.
Supporters have been forced to watch from home during a nightmare campaign which saw the club dethroned as Premiership champions.
The Trust proposed issuing shares instead of refunding season tickets for missed matches with the club initially stating punters would receive "added value" for their purchase.
But a statement from the group claimed Celtic had turned it down while insisting the "added value" pledge had been met.
This was due to extra matches including a League Cup match and UEFA being shown as part of the 'Pass to Paradise' package.
The statement from the Trust read: "The Celtic PLC Board, in the form of the Company Secretary, has responded to the formal proposal put by the Celtic Trust to them to offer shares to 2020-21 season ticket holders by way of meeting their obligation to provide added value as per their statement dated 23/6/2020 [23 June Celtic statement]. The letter acknowledged receipt of a copy of the advice provided to the SFA regarding the contractual issues around season tickets during the pandemic from the Society of Chief Officers of Trading Standards in Scotland [ST contract advice from Trading Standards].
"The letter contained a rejection of the proposal and the reason given was that the Trust had proposed a value for the issue which would not be possible under the existing authority (derived from a 2020 PLC AGM resolution) to issue shares on a non-preemptive rights basis. Moreover, they indicated that they had taken advice and that the cost of the management of this process would be in excess of £1,000,000.
"The entire premise of the rejection however, is false, given that there was no value indicated by the Trust in the formal proposal. Had they discussed the matter with us in February or March (something they explicitly refused to do) this could have been discussed and a more modest but meaningful value could have been agreed.
The Trust has written to the PLC expressing our disappointment at their refusal to consider the proposal in a genuine and meaningful way and the extremely discourteous way they have treated the Celtic Trust (and, by extension, all of its’ members and the members of other organisations which supported this proposal) by refusing to meet with us to discuss this proposal at any time between February and late May before rejecting it outright.
"In the letter, the Company Secretary, expressed the position of the PLC Board that they had already provided added value and were continuing to discuss ways to provide additional value. The added value they say they have provided consists of a stream for a league cup game, two friendlies, two delayed European games (after they’d finished) and online programmes.
"The Celtic Trust does not agree that any value has been provided which would meet the terms of the commitments made in June 2020 and we are also clear that no meaningful consultation has taken place given that no alternative proposals have been put to anyone by the PLC Board.
"We are extremely disappointed that the PLC Board has behaved in such a disrespectful and uncooperative way and we await their decision on how they will meet their obligations under the June 2020 statement.
"We believe the board have adopted an incredibly risky strategy which could have serious repercussions for the financial health of the club. However, it remains to be seen whether this gamble will pay off in terms of season ticket renewals or not."