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Hardliners in the Order are reported to be considering the unprecedented action because Mr Trimble broke its rules by attending a service in a Catholic church.
On 19 August, the Ulster Unionist leader and his party chairman, Dennis Rogan, were among several Orangemen who attended the funeral mass at St Mary's Church in Buncrana, County Donegal, for eight-year-old Oran Doherty, James Barker and Sean McLoughlin, both 12.
The funeral was also attended by the Irish President, Mary McAleese, and the Sinn Fein President, Gerry Adams, along with thousands of mourners.
Mr Rogan justified his decision to attend the service, saying it was the right thing to do.
'Essential' to pay respects
"Following the dreadful events in Omagh I felt that it was essential that on behalf of the Ulster Unionist Party, respect be paid to all the families of the deceased irrespective of their religious denomination," said Mr Rogan.
"Oran Doherty, Sean McLaughlin and James Barker were the innocent victims of one of the most brutal terrorist atrocities ever seen in Northern Ireland. What happened to them could have happened to any of our children.
"In a time of great suffering for the entire community, as chairman of the Ulster Unionist Party and in a personal capacity I believed then, and still do now, that it was the right and Christian thing to do."
'Popish worship'
One of the rules of the Orange Order is that "you should not countenance by your presence or otherwise any act or ceremony of Popish worship".
But it is highly unusual for action to be taken against members for attending Catholic funeral services, especially in border counties like Donegal.
Mr Rogan's lodge in Belfast is likely to be the first to take action. Mr Trimble's lodge in Bangor, County Down, could then follow suit.
A spokesman at Orange Order headquarters in Belfast said any disciplinary proceedings and would be a matter for individual lodges.
Talks
On Thursday night UK Prime Minister Tony Blair was reported to have held telephone talks with Mr Trimble and Sinn Fein leader Gerry Adams in a bid to clinch an agreement on elements of the new Northern Irish Assembly.
Mr Blair was said to be "absolutely determined" to get a deal before the Christmas break.
Mr Trimble and Mr Adams also held private talks described as "open and frank".