It is the clearest indication yet that officers are preparing for the possibility of a return to a hard border on the island.
Assistant Chief Constable Stephen Martin said: “The PSNI has a responsibility to keep people safe and we constantly review our resources to ensure that we are best equipped to do this.
“In light of the UK Referendum vote to leave the EU, we are reviewing decisions we previously made about our stations identified for disposal.
“Accordingly, it is our intention to pause the disposal of three stations in border areas, namely Warrenpoint, Castlederg and Aughnacloy.
“As the PSNI has not yet received details regarding potential border arrangements, this is a precautionary step to ensure that, whatever Brexit look like in the future, we will be able to continue to keep our communities safe,” he added.
Northern Ireland is the only part of the UK to share a land boundary with another EU member state – the Republic of Ireland.
Theresa May’s commitment to avoiding physical infrastructure at the border is difficult to square with her government’s determination to leave the Customs Union and Single Market.
Irish Prime Minister Leo Varadkar has said there needs to be a deal on the issue at the EU Summit this month if there is to be progress on a withdrawal agreement.
SDLP Brexit spokesperson Claire Hanna MLA said the postponement suggested “a willingness by some to accept a hard border”.
“The British government continually say that there will be no hard border in Ireland but they have failed time and time again to put a comprehensive plan on the table and this is the outcome of that indecisiveness.
“Any hardening of the border would be a deliberate violation of our political process by the British government.
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“Brexit is a real threat to our way of life. Any suggestion of any border here must be resisted. The socio-economic and the political consequences of a border across Ireland are catastrophic.
“Time is up for the British government. We can no longer wait on their pandering to hard Brexiteers. They must bring a solution urgently to ensure our way of life and the peace process is protected,” she added.