With an estimated price tag of up to 1.5 million euros ($1.7 million), Duranthon, who directs the Toulouse Museum of Natural History, said the skeleton would cost 20 to 25 years of his acquisitions budget.
"We can't compete," he said.
The triceratops is among the most distinctive of dinosaurs due to the three horns on its head -- one at the nose and two on the forehead -- that give the dinosaur its Latin name.
"Big John" is the largest known surviving example, 66 million years old and with a skeleton some eight metres long.
It was discovered in South Dakota in 2014 and flown to Italy where it was assembled by specialists.
It is only the latest dinosaur to be sold by the Drouot auction house which, according to its website, handled an allosaurus and a diplodocus each worth 1.4 million euros in 2018.
Last year, they sold a second allosaurus for three million.
That these and other skeletons could adorn the private mansions of the ultra-wealthy rather than museum halls is a common source of frustration.
For Steve Brusatte, a consultant on the forthcoming "Jurassic World" movie, "dinosaur fossils belong in museums".
The author of "The Rise and Fall of the Dinosaurs" remembers being a teenager and seeing the fossil that would inspire him to go into palaeontology.
"The T. rex skeleton Sue was put on display at the Field Museum in Chicago," Brusatte said.
"It awed me and, standing under it, it gave me a new perspective on the ancient world."
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