Some of the words of the national anthem are not "inclusive" and might need replacing, the ex-minister leading a citizenship review for Gordon Brown has suggested.
Former attorney general Lord Goldsmith said there was a problem with later verses of God Save the Queen and that some people were arguing for a change.
"There's some problem with part of it absolutely," he told Sky News.
"Part of it is not actually that inclusive but that's if you go onto the later verses. Some people have suggested we might think about whether there are different words that might be put in place which would be more inclusive."
Lord Goldsmith, who quit the Government when Tony Blair left office in June, said strong feelings about national symbols had to be taken into account.
Welsh Labour MP Ian Lucas is leading a campaign to include the principality's Red Dragon in the Union Flag to represent its "true place in the Union".
Asked if he backed the proposal, Lord Goldsmith said: "Well I think the Union Jack is understood and there's enough there but it's absolutely right, if there's a strong view about all these different symbols of nationality then they are things that we ought to know about."
He also spoke about the search for the British "statement of values" being sought by the Prime Minister - although he said some reports it should be as short as five words were optimistic.
In a package of constitutional reforms published in July, Mr Brown called for a citizen's summit to draw up a British statement of values, which would be "a living statement of rights and responsibilities for the British people"
The document - which is expected to be significantly longer than the proposed motto - would feed into a possible new British Bill of Rights.