According to The Sun, the substance Dettori tested positive for is believed to be cocaine.
Dettori's solicitor Christopher Stewart-Moore said: "On behalf of Frankie Dettori I can confirm that, as a consequence of a positive test at Longchamp on September 16, 2012, he will be the subject of an inquiry by the Medical Committee of France Galop next week.
"In compliance with, and out of respect for, the regulations of France Galop, he will not be commenting further until the France Galop procedures are completed."
The test took place during trials for the Prix de l'Arc de Triomphe and Detorri could be banned for up to six months if the inquiry finds him guilty.
A source added to the newspaper: "Frankie has failed a test for a banned substance which is thought to be cocaine. This is obviously very serious for him."