The IOC, which has struggled to attract prospective hosts given the enormous cost of staging the Games, did not want to turn either city away.
So IOC chief Thomas Bach pushed a plan to have both 2024 and 2028 awarded together at the organisation's main annual meeting in Peru in September.
That proposal, endorsed by Olympic executives last month, is expected to be rubber-stamped by the IOC's roughly 100 members on Tuesday.
With no other cities in the running, the vote would effectively guarantee hosting rights to Paris and Los Angeles.
And it looks increasingly likely that Paris will go first.
The French side has insisted it was exclusively focused on 2024, the centenary anniversary of the last Games in Paris.
Los Angeles, which last hosted in 1984, has indicated it was open to waiting four more years.
Both bids came to Lausanne with top-level political support.
French President Emmanuel Macron, who has been a vocal advocate of Paris 2024, met IOC top brass on Monday on a tour of the Olympic Museum, set on a hilltop overlooking Lake Geneva.
Macron portrayed the Olympics as a beacon of hope amid a deeply trouble political climate.
"In a fractured world where tensions are resurgent, we need the values of peace and tolerance that the Olympic movement illustrates and embodies strongly," Macron told reporters.
Los Angeles mayor Eric Garcetti, like Macron avoided commenting on a battle over 2024, but described the Olympic movement as a "good and true" force during "this crazy moment in the world."
The mayor, a prominent member of the US Democratic Party, toured the museum ahead of Macron, accompanied by a team that included Los Angeles bid chief Casey Wasserman and former sprint champion Michael Johnson.
He told reporters his goal was to "bring America back to the Olympics and the Olympics back to America".
Both cities will aim to sell their bids at Tuesday's IOC meeting, with Macron likely speaking as part of the French presentation.
Bach has already endorsed Paris and Los Angeles as model hosts, praising their efforts to trim costs by using existing or temporary venues, something the IOC hopes will become a growing trend.
The Olympic movement has been stained by Games that erected grand multi-million dollar facilities that were left to crumble and rot.
"It truly is a tale of two great Olympic cities," said a report released last week by the 2024 Evaluation Commission.
Bach said Monday he was eyeing a "win-win-win" result from the 2024 bidding process, with Paris, Los Angeles and the IOC emerging victorious.
Assuming IOC members approve the double-hosting plan, Bach said formal discussions will begin with both camps, with a goal of reaching consensus on which city goes first.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)