Those affected include the Lyric Theatre, the MAC, Playhouse Theatre in Londonderry, the Grand Opera House, NI Opera and the Ulster Orchestra.
The Arts Council's own budget was cut by 11% in March.
It has now been asked by the Department of Culture, Arts and Leisure (DCAL) to prepare for further cuts.
As a result, it has asked its major clients to consider how they might save money.
In a letter to each of the 32 organisations, the chief executive of the Arts Council, Roisin McDonagh, said that the cuts were deeply concerning.
She said that asking the organisations to plan for cuts of eight to 10% "is both a necessary and prudent request".
"Accordingly we would ask you and your board to to consider how you might apply up to an indicative 10% cut in your current year's grant from the Arts Council and assess the impact this will have on your programmes, staffing, services, audiences/participants etc," she said.
"I would be grateful if you could furnish us with this information by Thursday 20th August."
However, the letter also said that the Arts Council is awaiting "clarity" from DCAL on any cuts.
All of the affected organisations get substantial core funding from the Arts Council's revenue funding stream, which is money the council receives directly from DCAL.
For example, the MAC was awarded £950,000 in 2015/16, NI Opera got £561,569 and the Crescent Arts Centre £226,800.
This grant allows each organisation to pay staffing and building costs, and put on shows, exhibitions, events and concerts.
However, as the money is paid in stages, each organisation may not now receive its full grant allocation.
It is understood that if the planned cut goes ahead, some will have to shed jobs and cancel shows and performances.
A spokesperson for the Arts Council said that they were being asked to plan for cuts so had no option but to ask arts organisations to do the same.
The Arts Council has told 32 of Northern Ireland's largest arts organisations to plan for in-year cuts of up to 10% to their budgets.