DUP Minister Arlene Foster said Sinn Féin "should be careful what they wish for", adding the outcome of constitutional vote in Northern Ireland would be a "resounding" support for maintaining the union with Great Britain.
Sinn Féin President Gerry Adams recently launched a renewed campaign calling for a referendum on Irish reunification during the next Stormont Assembly term.
Ms Foster said discussions are ongoing with party colleagues, including leader and First Minister Peter Robinson.
She said the DUP has been considering supporting the so-called border poll because the party are confident the outcome would not be in Sinn Féin's favour.
In a statement, the Fermanagh and South Tyrone MLA said Sinn Féin's campaign was destabilising and polarised the electorate.
"Gerry Adams knows well that the overwhelming majority in Northern Ireland want to remain part of the United Kingdom," she said.
Ms Foster said the economics of a united Ireland didn't make sense.
"Northern Ireland currently receives a £10bn subvention from the Treasury. There has never been a rational argument put forward as to how this gap would be filled."
If such a destabilising and polarising message continues to be pushed then we may call their bluff. We may put an end to this foolish talk once and for all.
Arlene Foster, DUP Minister
She added: "Those who are advocating a poll could get a clear answer but it will not be the one they want."
She said the DUP is discussing the issue but has not reached a conclusion on the matter.
A referendum rejected a united Ireland in 1973. The poll was overwhelmingly boycotted by nationalists at the time.
Under the terms of the Good Friday Agreement, a poll can be called if there is evidence indicating support for a constitutional change.
A spokeswoman for NI Secretary of State Theresa Villiers said that the UK Government had no present plans to call a referendum based on recent election results and opinion polls.
"It is crucial that political leaders here concentrate on working together on pressing economic and social issues, including the rebalancing of the NI economy and building a genuinely shared society, rather than being diverted into divisive constitutional debates," the NIO said.
"We believe that political attention is really better focused elsewhere."
But Sinn Féin MLA Mitchel McLaughlin said the time was right to seek a referendum.
He said the party wanted to "provoke clear, radical and open debate in regards to the social, economic and political benefits of a united Ireland."
"Sinn Féin is ready for this debate. It is a debate that must be had if we are to manage the change that is already happening within Ireland and ensure that rights and entitlements for all are safeguarded and upheld.
It is time for a dialogue on how we heal the hurt, and move into a new era.
Mitchel McLaughlin, Sinn Féin MLA for South Antrim
East Belfast Alliance MLA Chris Lyttle said the timing was "inflammatory" in the current climate of loyalist flag protests across Northern Ireland.
"Sinn Féin should not proceed with this campaign but rather should reassure the community of their commitment to buildings a united community and shared future in Northern Ireland. This is not going to happen while Sinn Féin are using the language of a border poll," he said.
"There is no possibility of it taking place or having the outcome they desire at this stage.
"The support for the Good Friday Agreement and recent census results show this is the desire of the majority of Northern Ireland. Even the Irish Government have said that the conditions have not been reached for a border poll to be called," he said.
UUP MLA Tom Elliott described Sinn Féin's campaign as a "divisive, political stunt".
"Sinn Féin's call for a border poll is nonsense, designed to destabilise the current political arrangements," the Fermanagh and South Tyrone MLA said.
"The Ulster Unionist Party has nothing to fear from a border poll, but Sinn Féin should move on and stop wasting time and money.
"It also exposes the hypocrisy of Sinn Féin`s position; on one hand calling for a shared future and on the other demanding a divisive border poll."
SDLP leader Alasdair McDonnell said his party welcomed the opportunity for opinion to be gathered on a united Ireland but also had concerns on the timing of Sinn Féin's campaign.
"At this very difficult time we need to recognise that mutual respect, dealing with the past and meaningful reconciliation is the only way to build a prosperous future for everyone on this Island," he said.
"All parties must rise above selfish party interest when advocating reunification. The SDLP are committed to seeing a united Ireland but this is underlined by a real need to engage in debate about what the New Ireland will look like and how we can deliver that for the good of all our citizens."