The question of Mr Trump visiting Scotland comes after an anonymous source from Prestwick Airport said that an American military version of the Boeing 757, an aircraft often used by the Vice-President and the First Lady, is scheduled to arrive at the airport on January 19, the day before Joe Biden takes over the presidency.
Mr Trump owns the Turnberry golf resort in Ayrshire as well as another course in Aberdeenshire.
Speaking at Tuesday’s daily coronavirus briefing, Ms Sturgeon said that she “has no idea what Donald Trump’s travel plans are” but that she hopes that the only immediate plans he has are to exit the White House.
She went onto say in her answer: “We are not allowing people to come into Scotland, without an essential purpose right now, and that would apply to him just as it applies to anybody else and coming in to play golf is not what I would consider to be an essential purpose”
Airport sources said surveillance planes appeared to lay the groundwork for Trump’s arrival in November, last year.
The White House has downplayed the speculations that the current President will be travelling to Scotland on January 19.
Judd Deere, the deputy White House press secretary, told Fox News: "Anonymous sources who claim to know what the President is or is not considering have no idea.
"When President Trump has an announcement about his plans for January 20, he will let you know."