Flying the Union flag from the cenotaph at Belfast City Hall would be an acceptable compromise, the Alliance Party said today.
Maire Hendronsaid she was likely to back the proposal when it comes before a committee meeting in the New Year.
She said: "It is a reasonable proposition and I am not ruling it out.
"I probably would when the time comes following discussion with our party."
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Guillier conceded a "severe defeat" defeat to his supporters as the result came in.
The outage struck Hartfield-Jackson Atlanta International Airport at around 1pm local time, stopping all outgoing flights.
It will be a chilly day for many parts with the highest temperatures, about 10 Celsius (50F) in the far northwest.