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The presidential memorandum will give the Department of Homeland Security (DHS) and other agencies six months to establish the centre, an administration official told CNN.
According to the official, the centre is intended to streamline vetting and improve the flow of information between various federal agencies.
However, the memorandum will not establish any new authorities or call for any new funding to establish the centre, which will be an effort between DHS, the State Department, Justice Department and intelligence agencies, a National Security Council official said.
It remains unclear how this effort will change the way travellers and immigrants to the US are vetted.
The National Vetting Centre is part of the Trump administration's broader efforts to tighten immigration screenings, following Trump's calls for "extreme vetting" while campaigning in 2016.