0642 GMT August 18, 2018
The pushback came after Trump tweeted on Friday that he turned down the distinction, because the magazine did not guarantee him the spot, presstv.com reported.
"Time Magazine said that I was probably going to be named ‘Man (Person) of the Year,’ like last year but I would have to agree to an interview and a major photo shoot. I said probably no good and took a pass. Thanks anyway!" the president tweeted.
The magazine issued a statement disputing Trump. "The President is incorrect about how we choose Person of the Year. TIME does not comment on our choice until publication, which is December 6," a spokeswoman told CNN.
Time's chief content officer, Alan Murray, also shot back at Trump from his own Twitter account.
Trump said it was a ‘tremendous honor’ after he was named Time's ‘Person of the Year’ in 2016, one month after he defeated Democratic candidate Hillary Clinton in the US presidential election.
Trump has previously criticized the magazine for not being selected in past years.
"Thank you @oreillyfactor for your wonderful editorial as to why I should have been @TIME Magazine's Person of the Year. You should run Time!" Trump tweeted in December 2015.
In December 2012, Trump tweeted, "I knew last year that @TIME Magazine lost all credibility when they didn't include me in their Top 100... "
Fake Time cover featuring Trump has been spotted hanging at five of the president's clubs.
Trump has long been obsessed with being on the cover of TIME and other news magazines, even making fake covers to hang in some of his properties.
In June, The Washington Post reported that at least four Trump Organization properties had on display a fake Time magazine with Trump on the cover and featuring flattering headlines about his reality TV show, ‘The Apprentice.’