The two clubs reached an agreement on Monday for the 19-year-old defender to return to the Ligue 1 club on loan for a second successive season.
But St. Etienne claimed Arsenal did not finalise the paperwork before the deadline on Tuesday.
"Unfortunately, all the administrative conditions could not be met in time, in England, for the finalization of the file.
"There is a great disappointment for ASSE and William Saliba, who was particularly determined to return to the club where he had flourished."
However, Sky Sports state that Arsenal are pointing the finger at St. Etienne.
The Gunners believe that as the receiving club, St. Etienne were supposed to submit registration details first, but failed to do so.