Plans for the £96,000 raised tomb, unveiled last week, were initially well received by the society. Chairman Dr Phil Stone described them as “utterly inspired”.
But today the society confirmed several members had been in touch to request their donations not be used to fund the current design.
The plans would see Richard laid to rest in a raised tomb of fossil limestone with a deeply carved cross, on a floor inlaid with a large white rose.
Dr Stone said: “The authorities in Leicester Cathedral know that the Society has been collecting money towards the cost of the tomb for King Richard, but now that members are telling us that they do not want their donations given to support the present design, the executive committee of the society will need time to sit down and discuss the matter.
“I understand that the cathedral have stated that they will welcome anything that we can contribute financially but that they will not be held ‘hostage’ by us over the design.
“Since we have only sought to advise and have no intention of holding them hostage for the design and the money, there is nothing here to discuss.
“Also, of course, while there is doubt about where King Richard will be reinterred, all is speculation. When we know for certain which religious house will have the honour, that will be the time for further discussion and consultation.”
Peter Hobson, cannon missioner at Leicester Cathedral, told historyextra: “We are really not getting worked up about this.
“This money is in the custody of the Richard III society. We have never seen it and we have never banked on seeing it.
“When the body was confirmed as that of Richard, two things happened: the society moved to say he must be reinterred in a way they would like, and then a few members designed their own version of the tomb and had a collection for it.
“It became evident the design was not likely to command support, and we have not been able to support it. It would have been unusual if we had.
“We have submitted our design to the Cathedrals Fabric Commission for England (CFCE) and when that process is complete we will invite people to contribute to the tomb.
“Our design is very thought through, but the response has understandably been mixed. Some people say they like it while others say there are elements they don’t like.
“We want to take the Richard III Society with us if we can, but it would be unrealistic to say we can carry everyone.”
Richard’s skeleton was discovered underneath a Leicester council car park last September, 527 years after he was killed at the battle of Bosworth.
The remains were in February identified as those of the last Plantagenet king and, as an organisation closely involved in the discovery, the University of Leicester holds a Ministry of Justice licence that allows it to decide where the remains are reinterred.
The university decided on Leicester Cathedral.
Last month a High Court judge gave permission for descendants of the king’s relatives to challenge plans to rebury his remains in Leicester rather than York.
The 15-strong Plantagenet Alliance wants the remains buried in York, which, it claims, Richard regarded as his home.