Last year Trump told a reporter that registering people could be achieved through "good management procedures"
Donald Trump's transition team has denied the President-elect has ever advocated for a system of tracking Muslims in the US.
It comes as comments from two prominent Trump backers indicated that the concept of registering the details of anybody arriving from the US from Muslim countries could still be considered.
In a statement quoted by The Guardian, Trump team communications director Jason Miller said: "President-elect Trump has never advocated for any registry or system that tracks individuals based on their religion, and to imply otherwise is completely false.
"The national registry of foreign visitors from countries with high terrorism activity that was in place during the Bush and Obama administrations gave intelligence and law enforcement communities additional tools to keep our country safe, but the president-elect plans on releasing his own vetting policies after he is sworn in," the statement adds.
However, a video of Mr Trump on the campaign trail from last November has been highlighted as potentially contradicting the claim.
Responding to a question about a database system for Muslims, the then Republican hopeful said: "There should be a lot of systems - beyond [a] database. We should have a lot of systems, and today you can do it. Right now we have to have a border, we have to have a strength, we have to have a wall."
When pressed on the matter, he said: "I would certainly implement that, absolutely [...] It would stop people from coming in illegally." However, there was some ambiguity to the exact measures he was referring to - a database or more general border & immigration control.
He added that the registration could be achieved with "good management procedures", and that people could be signed up at "different places".
A few days later Trump took to Twitter to dismiss the claims he was advocating for a database.
I didn't suggest a database-a reporter did. We must defeat Islamic terrorism & have surveillance, including a watch list, to protect America— Donald J. Trump (@realDonaldTrump) November 20, 2015