Reuters could not immediately confirm the report, and representatives for Trump did not immediately reply to a request for comment.
The California city is seeking to host the summer Games for a third time in a bid that centred on celebrating diversity.
It had been seen as the front-runner in the race with Paris and Budapest until Trump's election this month after a highly divisive contest against Democrat Hillary Clinton that left the nation deeply divided and stoked fears about the future among some immigrants and minorities.
Last week, Los Angeles bid leaders urged officials at an Olympic meeting not to doubt the United States or its commitment to its founding principles and strength.
Garcetti, who supported Clinton, had previously said Trump's win after a campaign filled with harsh rhetoric toward immigrants, Hispanics, Muslims and women could be detrimental given the international makeup of the 98 voting members of the International Olympic Committee (IOC).
The IOC is set to make its selection in September 2017. Los Angeles, the nation's second-most populous city with nearly 4 million people, hosted the Olympic Games in 1932 and 1984.
Llanos, in a statement, said Trump's conversation with the mayor was short, and that Garcetti also "stressed the important role that immigrants and immigration reform will play in L.A.'s - and the nation's - long-term success," NBC said.
(Additional reporting by Roberta Rampton in West Palm Beach, Florida; Writing by Susan Heavey; Editing by Chris Reese)
