So far, she has remained publicly silent on the issue. But having made her views public in 1977 when Scotland and Wales were voting on devolved national assemblies, should she do so again, or could her intervention be ultimately damaging to the reputation of the monarchy?
She should hold her peace, says Peter Bingle, founder, Terrapin Communications
Those MPs and others who have argued for the Queen to involve herself in the referendum debate have clearly not thought through the implications for the future of the monarchy if there is then a Yes vote.
It would be a public humiliation for the Queen and a massive slap in the face for the PM, who would have advised her to do it.
It is bad enough for the PM that he has needlessly risked the future of the Union. Does he really want to be remembered as the PM who destroyed the British monarchy as well?
The whole point of a constitutional monarchy is that the monarch has huge symbolic power but in reality not much else apart from the odd castle or two. Why risk everything by making an anodyne statement on the importance of the Union? It just doesn't make any sense.
This isn't quite 1848 in France when Louis Philippe was deposed and replaced by Louis Napoleon (later Napoleon III) but the advisers to the Queen will be aware that these are turbulent times. The Queen should say nothing whatsoever or a difficult constitutional situation could become explosive.
She should stand and be counted, says Ross Cypher-Burley, senior account manager, Portland Communications
A Yes vote in the forthcoming Scottish referendum will mark the breakup of the UK. It will be a disaster. Not just economically, politically or even constitutionally. It would be damaging for the Queen herself.
As the consequences of a Yes vote became painfully clear over the following months and years, the public will clamour to know why the Queen – so trusted with the nation’s wellbeing – did not intervene when she was so firmly against the idea. Nationalists argue her intervention wouldn’t be appropriate. Not so. The Queen traditionally remains above politics, but has a duty to protect the union.
There’s precedent too. During her Silver Jubilee speech in 1977, she made a direct reference to those who had "aspirations" to have devolved national assemblies. Having said she understood such aspirations, she added: "But I cannot forget that I was crowned Queen of the United Kingdom of Great Britain and Northern Ireland. Perhaps this Jubilee is a time to remind ourselves of the benefits which union has conferred, at home and in our international dealings, on the inhabitants of all parts of the United Kingdom."
Throughout her reign, the Queen has demonstrated time and again a remarkable ability to judge the mood of the nation. She’s trusted. She attracts none of the cynicism that follows modern politicians. An appeal from Her Majesty would show leadership. It would be understood by the public that she was intervening not out of political calculation, but in the national interest. Remaining silent on the referendum threatens the selflessness that the Queen embodies.