It is reported that the video, which was filmed in the early days of his successful presidential campaign in August 2015, shows the Spanish-speaking journalist being escorted from the event, after challenging the future president on his immigration policies.
Jorge Ramos, a well-known broadcaster for Univision, is caught off-camera attempting to raise a point to Mr Trump.
The journalist said: “I am a reporter and I have a right to ask a question…”
But Mr Trump swiftly interjected him, responding: “Excuse me sit down, you weren’t called, sit down.
Jorge Ramos claimed a Trump aide told him to "get out of the country"
How are you going to deport 11 million people?
“No you don’t [have the right to ask a question], go back to Univision.”
Mr Ramos adds: “You cannot deport 11 million people, you cannot build a 1,900-mile wall, you cannot deny citizenship in this country.”
He is then seen being escorted out by one of Mr Trump’s staff, despite remonstrating with the aide let to him stay.
Mr Ramos, once outside the room, then claims Mr Trump’s aide, who had reportedly never heard of him and wasn’t aware he was American, told him to “get out of my country”.
When the reporter responded that “I am also a US citizen”, the aide dismissed him and said: “Univision, whatever.”
Univision is a USA-based Spanish-language broadcaster.
Mr Ramos was later allowed to re-enter the press conference, where he asked: “How are you going to deport 11 million people? Are you going to bring in the army?”
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To which, Mr Trump replied: “We’re going to do it in a very humane fashion. Believe me. I have a bigger heart than you do.”
Being President Trump: Key Moments
Tue, January 31, 2017
Inside Donald Trump's first week in the White House.
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US President Donald J. Trump attends a meeting on cyber security, in the Roosevelt Room of the White House, in Washington, DC, USA, 31 January 2017
The reemergence of the footage comes after President Trump announced an executive order barring travellers from seven Muslim-majority countries entering the US for 90 days and refugees for 120.
The President has come under widespread international criticism for signing the order, which prevents immigration from Syria, Iraq, Iran, Yemen, Libya, Somalia and Sudan.
High-profile UK celebrities, such as Lily Allen and Gary Lineker, joined protests in London against the travel ban, which was also slammed by the Government.