The NI Assembly Commission has not reached a decision on two contentious events to be held at Stormont.
Farrell was one of three IRA members shot dead by the SAS
The cross-party grouping discussed the issue and adjourned its meeting until later in the week.
Sinn Fein plans to hold an event celebrating IRA member Maireád Farrell. The DUP plans an event to celebrate the SAS during the Troubles.
Farrell was one of three IRA members shot dead by the SAS in Gibraltar 20 years ago.
Earlier, the assembly speaker refused to take points of order about the proposed function in the chamber.
Some sources at Stormont have said the commission may have to look at the details provided by event organisers to the assembly about functions they wish to hold.
There were also suggestions that there could be a temporary freeze on politically contentious events in the Stormont Long Gallery.
Assembly member Jeffrey Donaldson is making the DUP application. He said Sinn Fein's plan should not go ahead.
"I believe we should celebrate the lives of role models but who in their right mind could view a terrorist who was prepared to kill innocent men, women and children as a role model?"
He added: "However, it is right and proper that we should celebrate and commemorate our armed forces who stood against terrorists such as Farrell."
DUP leader Ian Paisley led a party delegation to meet assembly speaker William Hay to discuss the proposed event.
Speaking after Monday's meeting, Mr Paisley said: "We had a useful and frank meeting with the speaker and my colleagues and I expressed in very forthright terms our opinion that this disgraceful proposal should not be given the go-ahead."
He added: "The DUP will oppose any commemoration for murderers in Stormont and will use all of our influence to prevent this event from taking place. I am confident that we are bringing closure to this issue."
Maireád Farrell was shot dead in Gibraltar in 1988 along with two other IRA members by the SAS.
Keys to a car found in her handbag led to the discovery in Spain of five packages of Semtex explosive.
Farrell had previously been jailed between 1976 and 1986 for the bombing of the Conway Hotel in Dunmurry, outside Belfast.
Sinn Fein assembly member Jennifer McCann said she planned the event commemorating her at Stormont to mark international women's day.
"Stormont is a shared space and that's the way it has to be seen," she said.
"The real thing about this and the honest thing about this is that Jeffrey Donaldson and unionists are saying that we have the audacity to pay tribute to our dead and they're trying to tell us when and where we can do it.
"In effect they're creating a hierarchy of victims."