"I guess, right? Covers, nobody's had more covers," Trump asked.
Scherer, who joined The Washington Post in September, told Trump that Richard Nixon "still has you beat." But he shouldn't worry because Nixon was president for longer, Scherer told the then-newly inaugurated president, adding that he should give himself more time.
"OK, good. I'm sure I'll win," Trump replied.
Some days, he relishes the recognition:
"On the cover of @TIME Magazine - a great honor!" he tweeted on Aug. 20, 2015.
"Time Magazine has me on the cover this week. Don Von Drehle has written one of the best stories I have ever had," he said on Jan. 9, 2016.
"Remember, get TIME magazine! I am on the cover. Take it out in 4 years and read it again. Just watch...," he tweeted the following day.
Last December, when Time named him Person of the Year, he told NBC News it "means a lot" and that he considers it "a very, very great honor."
On other days, however, he was more critical, including when the cover features someone else: "I told you @TIME Magazine would never pick me as person of the year despite being the big favorite They picked person who is ruining Germany," he tweeted on Dec. 9, 2015, when the magazine named German Chancellor Angela Merkel Person of the Year.
That was followed by a tweet later that day thanking then-Fox News host Bill O'Reilly for a "wonderful editorial" on why Trump should've been picked.
In December 2011, Trump criticized the magazine when it chose "The Protester" as its "Person of the Year" to highlight protests that had brought political and social change.
He was also highly critical of Time in May 2012, when it featured a mother breast-feeding her toddler, and again in July 2012, when Chief Justice John Roberts Jr. made the cover.
That same year, Trump said Time had lost all its credibility when it didn't include him in its Top 100 most influential people.
Indeed, the president places high value on seeing his face on magazine covers - and he likes to show proof of it.
Case in point: Many of his clubs are decorated with these covers - including, until recently, a fake March 2009 Time cover that featured the real estate developer and proclaimed: "TRUMP IS HITTING ON ALL FRONTS . . . EVEN TV!"
During a September 2015 interview with CBS's Scott Pelley in Trump's Manhattan penthouse, Pelley took note of magazines stacked on Trump's desk and pictures hanging on the walls of his office. All have his face on them.
"What are we supposed to take from that?" Pelley asked.
Trump replied with a grandiose proclamation.
"You know, look, I'm on a lot of covers. I think maybe more than almost any supermodel. I think more than any supermodel. But in a way that is a sign of respect, people are respecting what you are doing," he said.
But if history were any indication, a picture on a magazine's coveted spot isn't always tied to a positive story or "a sign of respect." Time, for example, has frequently featured unflattering photo illustrations of Trump, both when he was a candidate and president.
One of the magazine's covers in February is an illustration of the president sitting stoically behind his desk as a hurricane engulfs the Oval Office. Below the magazine's name: "Nothing to see here."
A cover from March features Trump typing on his phone while leaning on a crumbling Washington Monument. "Trump's war on Washington," the cover says.
More recently, earlier this month, a Time cover featured illustrations of the likeness of Trump's face shaped as wrecking balls.
Last year, in August and October, Time twice featured a likeness of Trump's face melting like candle wax to portray the then-candidate's tumultuous campaign. Each cover had the word "meltdown."
In March 2016, one of the magazine's covers was a black-and-white, zoomed-in face of Trump, with five check boxes across. The boxes for "bully," "showman," "party crasher" and "demagogue" were checked, while the box for "the 45th President of the United States" was left blank.
The title Person of the Year also is not defined solely by glowing coverage or positive recognition. The title is given to "the person or persons who most affected the news and our lives, for good or ill, and embodied what was important about the year, for better or for worse," former managing editor Walter Isaacson wrote in the 1998 issue.
The same nod has been given to Adolf Hitler in 1938, Joseph Stalin in 1939 and 1943 and Iran's Ayatollah Khomeini in 1979.
Trump was given the title last year for his unexpected victory against Hillary Clinton.