According to the UK-based media outlet, the plans were put in place after Police Service of Northern Ireland (PSNI) chiefs asked for "reinforcements to deal with any trouble that arises from a hard border." The drills for almost 1,000 officers are reportedly expected to begin this month.
Members of the UK Parliament are set to return from their Christmas break on 7 January, and a new debate over the Brexit deal is scheduled for 9 January. A vote on the deal is expected to take place the following week.
A spokesman for May said that the UK government had stepped up preparations for leaving the European Union without a deal.
A no-deal scenario means that there will be no transition period, and the United Kingdom would have to leave the European Union and abandon everything associated with it on 29 March 2019.