Neither has Donald Trump claimed to be a Nazi nor have any credible reports proven that he is one.
However, a glance at President Donald Trumps family history and personal background does not indicate any relationship with The National Socialist German Workers Party or 'Nazi Germany'.
The term 'Nazi' or 'Fascist' has often been used to describe President Trump's nationalism, policies, and condoning of authoritarian leaders around the world. On 12 August 2017 Trump offered a more forceful denunciation of the white supremacists and neo-Nazis who had rallied during the Charlottesville violence in Virginia. He had claimed that there were good people on both sides involved in the violence where some of the people in that rally protested peacefully while taking down the statue of Robert E. Lee. He had also pointed out that a few people were responsible for the actual violence. This was followed by widespread criticism as the white supremacists were also among the people the President claimed to be the good ones which resulted in the President being labelled as a Neo-Nazi sympathiser. But this, however, does not prove that he is actually a member of such an organisation or that he is its supporter.
Factually, President Trump is not a Nazi since the term refers to a specific section of German society and political leadership until the 1950s.