A working group of officers and members has canvassed views of member authorities and recommended that Cosla cuts its ties, depriving the LGIB of an annual income of about £110,000.
Cosla chief executive Douglas Sinclair has been asked to present members at a meeting on 13 September with a choice of dates for withdrawal.
Despite earlier assurances to the LGIB that Cosla would remain committed until the end of this calendar year, members are now expected to consider immediate withdrawal on financial grounds.
'It was felt by member authorities that there was a degree of duplication with the LGIB,' Mr Sinclair explained. 'Cosla already has a Brussels office and we have a dedicated European team of four.
'Clearly in terms of issues of a UK dimension affecting local government, we would work closely with the Local Government Association.'
LGIB director Jeremy Smith said he was disappointed at the recommendation, and questioned Cosla's ability to maintain the quality of work with its European and international staff of five.
Cosla's departure will almost certainly mean two vacant posts out of its 28 will be frozen, and shedding staff has not been ruled out.
The withdrawal of Cosla would deprive the LGIB of one of the key reasons for remaining separate from the Local Government Association: that it is the UK-wide voice of local government. It would be left representing the LGA and the Association of Local Authorities of Northern Ireland.
Another reason for remaining separate is that most of its budget of £1.6 million is 'top-sliced' from revenue support grant. If it was subsumed within the LGA this would be lost, and the LGA would have to increase its subscriptions to cover the cost of handling international work for local government in England and Wales.
The Welsh LGA has not ruled out handling its own European work in future.