"I am favourable if the city of Paris decides to present its candidacy," Hollande said in a French television interview Thursday night.
He listed advantages of hosting the Olympics, including the "fervour" it would create and the jobs it would generate.
But Hidalgo, a Socialist like Hollande, struck a far more cautious tone at a news conference Friday, citing failed Paris bids for the 1992, 2008 and 2012 Games.
"At this point I don't have the elements at hand to decide," she said. "There is no reason at this point to close a door or to open one. If there are dreams to share with the French, to share about the Olympics, I hope they can come true."
Paris hosted the 1900 and 1924 Olympics but failed in its last three bids.
"You need methods and you need to ask the right questions how to build a winning strategy," Hidalgo said. "I'm not into chasing dreams. ... I know what happens when dreams come unstuck against harsh reality. This is what happened in the last three candidatures."
Bernard Lapasset, who heads the French Committee for International Sport, said earlier this week that any decision on whether Paris might bid would not be taken before January,
"If we do commit then it's to win," Hidalgo said. "I am sticking to the January schedule. We must have a serious and rigorous method."
Hidalgo listed "three essential things" that are needed should Paris eventually bid.
"Ethics and transparency in the way we treat each city's dossier ... It's particularly costly," she said. "There have been cities which have been left with white elephants in the perpetual race for more and more."
Hidalgo said "a sound economic model" is needed because "a candidature can only be one which brings economic development."
Finally, the "environmental impact of the games" must be taken into account, she said.
Because of France's economic struggles, no public money will be spent if the country decides to go ahead with a bid next year, national Olympic committee president Denis Masseglia said on Tuesday.
A 24-hour telethon could be held in June to raise funds for a bid, which could cost up to 80 million euros ($100 million).
Lapasset said the outcome of the International Olympic Committee session in Monaco in December will be taken into account. IOC President Thomas Bach is proposing a series of reforms, including a revised bidding process and ways of making the games less costly.
Paris is among a number of potential contenders for the 2024 Games. The U.S. Olympic Committee is weighing a possible bid from either Los Angeles, San Francisco, Boston or Washington D.C. Germany is considering Hamburg or Berlin. Rome; Doha, Qatar; Istanbul, Turkey; Baku, Azerbaijan, and cities in South Africa are also interested.
The IOC will send out invitations for bids next year. The host city will be selected in 2017.