The event on Thursday morning will be a notable moment of recognition for Trump, a born-and-bred New Yorker who gave up living full time in his namesake Trump Tower in Manhattan and moved to Florida.
The US stock market soared after Trump won the 2024 election in part by seizing on worries over the economy.
The ringing of the bell is a powerful symbol of US capitalism - and a good New York photo opportunity.
According to the NYSE's calendar, Trump has never done it before.
The people who confirmed the bell-ringing were not authorised to discuss the matter publicly and spoke to the Associated Press on condition of anonymity.
It was not clear whether Trump, a Republican, would meet with New York's embattled mayor, Democrat Eric Adams, while in the city.
The stock exchange regularly invites celebrities and business leaders to participate in the ceremonial opening and closing of trading.
During Trump's first presidential term, his wife Melania Trump rang the bell to promote her "Be Best" initiative to promote children's well-being.
After the November 5 election, the S&P 500 rallied 2.5 per cent for its best day in nearly two years.
The Dow Jones Industrial Average surged 1,508 points, or 3.6 per cent while the Nasdaq composite jumped 3.0 per cent.
All three indexes topped records they had set in recent weeks.
The US stock market has historically tended to rise regardless of which party wins the White House, with Democrats scoring bigger average gains since 1945.
But Republican control could mean big shifts in the winning and losing industries underneath the surface and investors are adding to bets built earlier on what the higher tariffs, lower tax rates and lighter regulation that Trump favours will mean.
The ringing of the bell has been a tradition since the 1800s.
The first guest to do it was a 10-year-old boy named Leonard Ross, in 1956, who won a quiz show answering questions about the stock market.
Many times, companies listing on the exchange would ring the bell at 9.30am to commemorate their initial offerings as trading began.
But the appearances have become an important marker of culture and politics - something that Trump hopes to seize as he has promised historic levels of economic growth.
The anti-apartheid advocate and South African President Nelson Mandela rang the bell as has Hollywood star Sylvester Stallone with his castmates from the film The Expendables.
So too have the actors Robert Downey Jr and Jeremy Renner for an Avengers movie and the Olympians Michael Phelps and Natalie Coughlin.
In 1985, Ronald Reagan became the first sitting US president to ring the bell.
"With tax reform and budget control, our economy will be free to expand to its full potential, driving the bears back into permanent hibernation," Reagan said at the time.
"We're going to turn the bull loose."
The crowd of traders on the floor chanted "Ronnie! Ronnie! Ronnie!".
The Dow Jones Industrial average climbed in 1985 and 1986 but it suffered a decline in October 1987 in an event known as "Black Monday".
