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It is alleged to have happened when he attended a session where councillors could read the confidential report of the inquiry into the council's handling of complaints against senior social worker Sean Bell.
Susanne Tanner, the QC who led the inquiry, told a full council meeting last month that one councillor had "crossed the line of acceptable behaviour" by shouting at a junior female member of staff and said a letter of complaint would follow.
Now Julian Diaz-Rainey, partner in law firm Pinsent Masons, has written to group leaders and council chief executive Andrew Kerr setting out the allegations.
Councillor McLellan, who is an Evening News columnist and former editor of the paper, has totally denied the allegations, which he said were "entirely unsubstantiated", and said he was confident he would be exonerated.
The letter from Mr Diaz-Rainey said Councillor McLellan attended a session at Pinsent Masons offices along with fellow Conservative Joanna Mowat and Lib Dem Neil Ross.
And it referred to the councillors' dissatisfaction and Councillor McLennan's "discontent" at one passage in the report which expressed the inquiry team’s hope that its recommendations would not be used as "a political instrument", and went on to say it would not be in the interests of the council, or those whom it serves, for the report to be “seized upon by elected members or their parties and used for political gain".
The letter continued: "I am told that Councillor McLellan banged both of his fists on the table and shouted at XXX and XXX, ‘this is an absolutely outrageous comment to make.’
"He proceeded to exclaim that the inclusion of such a comment would, on the contrary, have the opposite desired effect and fuel the councillors’ political debates in the way in which the inquiry team hoped to avoid. Essentially the phrase was ‘like a red rag to a bull,’ or words to that effect. While stating his objection, I am told that Councillor McLellan raised his voice at the inquiry team.”
Mr Diaz-Rainey added that he did not object to Councillor McLellan’s desire to voice his dissatisfaction with words in the report.
"What I do take strong exception to is Councillor McLellan’s needlessly aggressive behaviour towards two junior members of my team. I am disappointed to hear that a meeting which was arranged to engender healthy discussion turned into one in which junior lawyers were shouted at and left feeling uncomfortable in the presence of Councillor McLellan."
Councillor McLellan said he totally denied the allegations and the conversation was witnessed by Councillor Mowat who was in full agreement with him.
He continued: "I have absolutely nothing to hide. I raised legitimate concerns about a section of the report which I still believe was beyond its remit and inappropriate and I was entitled to raise those concerns. These allegations are entirely unsubstantiated and in order to be independently exonerated I have reported this matter myself to the standards commissioner."
The council said it had been contacted by Pinsent Masons regarding the conduct of a councillor and it had also referred the matter to the commissioner for ethical standards.