The new Northern Ireland Office junior minister Kris Hopkins said the issue of flags in Northern Ireland was "a sensitive and complex one".
He said any change in arrangements would require cross-community support.
Saint Patrick's Saltire or Saint Patrick's Cross is a red saltire on a white field, used to represent Saint Patrick, the patron saint of Ireland. It has been represented in the Union flag since the Act of Union in 1801.
Meanwhile, the newly appointed Northern Ireland Secretary has moved to effectively rule out the possibility of a referendum on Irish unity. James Brokenshire told MPs he did not believe that the conditions required to call a border poll had been met. His comments, made during his House of Commons debut in his new role, came after Taoiseach Enda Kenny raised the prospect of a future vote on Irish unity in the wake of Brexit. The Irish premier said EU/UK negotiations should take into consideration the possibility that a border poll could be held in years to come.
But his intervention prompted fury from unionists.
Nigel Dodds, deputy leader of the DUP, asked Mr Brokenshire during Northern Ireland questions: "Can you spell out for the benefit of the House once again what you have already said publicly in Northern Ireland, why there is no question of a border poll in Northern Ireland?"
Mr Brokenshire replied: "I have been quite straightforward in relation to the issue of the border poll. The conditions are set out clearly in relation to the Belfast Agreement and I have been very clear that I do not think those conditions have been met."
Under the terms of the peace agreement the power to call a border poll rests with the Secretary of State.
But the accord stipulates that such a vote can only be called if there is evidence of a clear shift of public opinion in favour of Irish unity in Northern Ireland.
The issue of a poll has been the subject of renewed debate after Northern Ireland voted to remain in the EU in the face of the UK's decision to leave. Mr Dodds added: "The reason that it hasn't been met is because the overwhelming majority of people in both communities in Northern Ireland want to remain part of the United Kingdom."