Two of the smaller headlines – which promise stories on President Barack Obama, climate change, and the financial crisis – were taken from the genuine March 2, 2009 edition of Time, whose cover star was Kate Winslet.
Time has said there was no March 1, 2009 issue of Time, and Donald Trump did not feature on the magazine’s cover that year.
A spokesperson said the magazine had asked the Trump Organization to remove the fake cover.
The Washington Post, which first reported the story, said the mock-up had been displayed in two spots at Donald Trump’s resort in Doral, outside Miami.
It also hung in the members’ dining room at the Trump golf course in Loudoun County, Virginia.
Photographer Scott Keeler tweeted a picture showing it on the wall of the Mar-a-Lago club in Palm Beach, Florida.
The post also states that Donald Trump “is not the first president to have access to Mar-a-Lago as a Florida retreat, but he is the first one to use it.
“By visiting this <<winter White House>>, Trump is belatedly fulfilling the dream of Mar-a-Lago’s original owner and designer.”
Since taking office, Donald Trump has spent seven weekends at Mar-a-Lago, which he bought in 1985 and turned into a private members club.
The president’s visits have led to concerns over costs and mixing business with politics.
The club has raised its initiation fees from $100,000 to $200,000 following Donald Trump’s election.
Since President Trump’s inauguration, Democratic groups and ethics watchdogs have been monitoring whether there has been a potential conflict of interest that could benefit his business holdings while he is in office.
In December, Donald Trump announced that he planned to shut his charitable foundation, although an investigation into its practices continues.