The Kempinski Hotels group, which runs more than 60 five-star hotels around the world, is to manage the Crillon, the paper said, but the new acquisition would be its first in France.
The Crillon, built in the 18th century on what would become the Place de la Concorde, has 147 rooms and suites and employs around 360 people.
Views from its rooms give on to the site where King Louis XVI and many others were guillotined during the aftermath of the 1789 French revolution. Today the hotel is next to the United States embassy.
Its best known suites are on the fifth floor, named after such luminaries as US composer Leonard Bernstein or Louis XVI's predecessor, Louis XV.
Starwood Capital and the Crillon declined to comment on the reported deal, which follows a months-long legal battle between Starwood Capital and former suitor JJW Hotels and Resorts, owned by Saudi Sheikh Mohammed al-Jaber.
Starwood Capital bought the hotel from the former Taittinger group in 2005, saying it wanted to launch a luxury hotel chain under the Crillon brand, but in 2008 the group changed strategy and said it wanted to sell its luxury assets.
Then, JJW was reportedly set to buy Starwood's luxury hotels for 1.5 billion euros, including 350 million euros for the Crillon, but the deal ended up in court with both sides accusing each other of breach of contract.
Starwood then decided to sell its luxury assets individually, selling Paris's Lutetia to Israeli group Alrov, although Starwood's Groupe du Louvre still manages the Left Bank gem.
Almost all of Paris's luxury hotels are now owned by foreign groups.
Saudi Prince Al-Waleed bin Talal owns the George V, Egyptian tycoon Mohamed al-Fayed owns the Ritz, the Sultan of Brunei's Dorchester group owns the Meurice and German group Oetker owns the Bristol.
The only luxury palace hotel still controlled by French capital in the French capital is Le Fouquet's Barriere.
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