Proposals for a neutral civic flag at Stormont have sparked unionist fury.
A consultants' report suggests the new flag could be flown at Parliament Buildings on days the Assembly is sitting.
But it also made clear the political parties would have to agree on any replacement flag or "some other visual display".
The report stated: "There is a chill factor for those from a nationalist or republican community which makes the building less welcoming on days when the Union flag is flying... it was reported that visitors (to Stormont) had regularly commented likewise."
The report for the Assembly Commission, which runs Parliament Buildings, said the potential for the flying of a neutral, civic flag had attracted some support, "especially among staff" working in the Assembly.
It said the Commission "might consider flying a neutral, civic flag (the nature of which would need to be agreed among the political parties) to mark days when the Assembly is sitting".
While supporting the status quo of the Union flag being displayed on designated days, the equality assessment report also argued: "It is evident that there are strong feelings in both communities about the flying of the Union flag and that any decision on the flying of the Union flag therefore has the potential to damage good relations."
It was commissioned by the Assembly Commission, which recently decided to extend the number of designated days on which the Union flag is displayed from 15 to 18 per year.
But the report also suggested that on designated days a new neutral flag could fly on a second flagpole alongside the Union flag.
Consultants Policy Arc also referred to the most recent Life and Times survey last year, which showed that 48% of Protestants and 59% of Catholics felt that the Union flag should be flown from public buildings on designated days only.
And it said legal opinion provided to Belfast City Council when it switched from all-year-round displays of the Union flag to designated days said "this policy...would be regarded as striking the right balance between acknowledging Northern Ireland's constitutional position and not giving offence to those who oppose it".
But unionists reacted with fury.
Paula Bradley, the DUP's representative on the Commission, said the proposal for a supposed neutral flag had been around for several months but her party wanted to see the Union flag flown at Parliament Buildings every day, adding: "Northern Ireland has a flag. It's called the Union flag. I would rather people accepted this reality and stopped placing so much focus on flags.
"To fly the Union flag every day would put us in the mainstream across the United Kingdom. Westminster flies the Union flag every day. The Welsh Assembly flies the Union flag every day alongside the Welsh flag and the EU flag. Indeed, even the Scottish Parliament with the Scottish nationalists' influence flies the Union flag alongside the saltire and EU flag every day."
And TUV councillor Andrew Girvin argued: "Given all the controversy there has been over flags and symbols in Northern Ireland, the very last thing we need is another flag introduced into the mix.
"To suggest that Stormont is somehow full of Unionist symbols which cause huge offence to nationalist visitors is, frankly, nonsense.
"Stormont is unique among the regional assemblies and national Parliament of the UK in not flying flags on a daily basis. Not only that, but huge parts of the Unionist history of Stormont have either been removed or are ignored."
Sinn Fein also rejected the proposal of a neutral flag, saying: "(We) support the flying of the Irish tricolour alongside the Union flag at Parliament Buildings in the interests of equality, parity of esteem and recognition and respect of both main traditions."