In an open letter to the Scottish legal profession, former BBC lawyer Alistair Bonnington questioned the handling of the society's move away from its current Drumsheugh Gardens base, which was abandoned last year after the owner of proposed new premises refused to drop the agreed purchase price.
This cost the society 97,688, including 32,644 to Brodies in legal fees and 39,818 to Jones Lang Lasalle for valuation and survey work.
In the letter, Mr Bonnington said he was "increasingly curious" about the relocation , after what he described as "conflicting information" appeared on the society's website.
He has laid down a motion to be discussed at a forthcoming meeting calling on the society to lay the full facts before its internal audit committee.
Responding to the request, the society said it would farm out the review to external auditors Henderson Loggie – a move that would incur a fee.
Mr Bonnington said: "Getting information from the society to its members over this relocation project has been like drawing teeth. Nothing comes out unless pressure is put on the society.
"My initial curiosity over this matter has become, I'm afraid, something like suspicion. These concerns can be allayed only by the matter going to the society's audit committee."
Mr Bonnington described the decision to employ external advisers as "extraordinary" and raised fears the results would be kept from members.
He wrote: "The council want the report from these auditors to go not to the membership as I had proposed, but back to the council, who will then decide what is to be disclosed to the membership. Why?"
Glasgow lawyer John Macmillan, who seconded the motion, said he believed the Law Society had had no intention of scrutinising the project until the matter was raised.
"The Law Society, as far as I know, had no plan in relation to this until the motion was made. They came back with an amendment to take it to external auditors. We don't see that as the best way of dealing with it, and certainly not the least expensive way of dealing with it."
The society hit back at the claims, insisting the decision was entirely proper.
Noting that any internal committee work would also incur a cost, a society spokeswoman said: "As the society's audit committee was involved in the relocation project, council believe that an external auditor should carry out the review."
The spokeswoman stressed that the decision on whether to commission an independent report had not been made and added: "The report, if commissioned, would be publicised, but not all the documentation associated with the move, as some of it is commercially sensitive."
The society confirmed that the relocation was still on hold, but would be reconsidered when market conditions improved.