The bid, which is competing against three European cities, risks an anti-U.S. protest vote by several IOC members angry over America's prominent role in pursuing doping allegations against Russian athletes, the sources said.
The IOC will decide on bids from Los Angeles, Paris, Rome and Budapest in September next year.
At least three non-Russian IOC members, speaking on condition of anonymity, said America's intervention into allegations of systematic Russian doping had marred the run-up to the Rio Games and tarnished the IOC brand.
"Of course the Los Angeles bid will face some consequences from this," an IOC member said.
The U.S. Department of Justice is probing allegations of Russian doping on U.S. soil, and the U.S. anti-doping agency (USADA) called for a total ban on Russians in Rio even as U.S. athletes with a history of positive drugs tests competed there.
None of the IOC members interviewed by Reuters could give an estimate of how many of the IOC's 98 members were thinking along the same lines. Elections for host cities can be decided by a handful of votes and be heavily influenced by politics.
Last year's vote for the 2022 winter Olympics was won by Beijing, with just four votes more than Kazakhstan's Almaty.
Russia alone has three IOC members.
The head of the LA 2024 bid team, Casey Wasserman, said it would not make sense for IOC members to vote against Los Angeles on the basis of investigations totally unrelated to its bid.
"Doping agencies in America are independent. They are not under the control of the United States Olympic Committee (USOC), they are certainly not under the control of a private independent bid which is what we are," Wasserman said.
"We are independent of USOC and of the city of Los Angeles, we are private and to somehow use that against us seems misguided," he added.
LA Mayor Eric Garcetti has acknowledged that there could be a backlash from some IOC members but has also distanced the bid from the actions of the other, independent U.S. bodies, such as the Department of Justice and USADA.
Another IOC member said a separate Department of Justice investigation into corruption at world football's governing body, FIFA, also rankled with some committee members, given close links between the two sporting bodies.
Several senior FIFA officials were arrested last year, woken up at their five-star hotel in Zurich and held in prison pending extradition to the United States over corruption and embezzlement charges.
IOC member Issa Hayatou of Cameroon is FIFA's senior vice president, while Sheikh Ahmad Al Fahad al Sabah of Kuwait, who is in charge of the IOC's central fund, the Olympic Solidarity, is a member of the FIFA council.
Neither of the two members, who declined to comment, has been named in relation to investigations of the FIFA cases.
Another IOC member said there would be "significant" fallout for the Los Angeles bid.
A Canadian lawyer's investigation into what he called systematic Russian doping led to the world athletics federation banning the country's track and field team, with the exception of just one athlete, from the Rio Games.
USADA had formed a coalition of anti-doping bodies calling for a blanket ban on all Russian competitors at the Games, but the IOC eventually cleared more than 270 Russians to compete.
Last month, United World Wrestling Federation President Nenad Lalovic, an IOC member and a member of the World Anti-doping Agency (WADA) board, made comments to Reuters that were indicative of the frustration felt by some IOC members.
"USADA should be focussed on the health of American athletes and those competing in the United States," Lalovic said.
"Now it seems that USADA and the Canadians took over responsibility of WADA. Nobody entitled them to do that."
(Editing by Mark Bendeich)
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