The Republican billionaire spoke by phone with Los Angeles Mayor Eric Garcetti and the two men had a "productive conversation," Garcetti's spokeswoman Connie Llanos said.
During the conversation Trump, who will succeed Democratic President Barack Obama on January 20, indicated his support for LA's bid, she said.
Los Angeles hosted the Summer Olympics in 1932 and 1984, and is competing with Paris and Budapest to do the same for the 2024 games.
The name of the 2024 host city is set to be announced in September 2017 in the Peruvian capital of Lima.
In last August, when Trump's chances of winning the White House looked slim, Garcetti warned that a victory by the outspoken populist would reduce the chances of Los Angeles being picked by the International Olympic Committee.