Saliba signed for Arsenal in a reported £25million deal last year before being loaned back to Les Verts for the 2019-20 campaign.
Although Ligue 1 was ended prematurely due to the coronavirus pandemic, the Coupe de France final is to go ahead on July 24.
Saint-Etienne will face Paris Saint-Germain in that contest and had hoped Saliba, 19, would be available for it, while Arsenal coach Mikel Arteta also expressed a desire for the France Under-20 international to have that opportunity.
But Saint-Etienne confirmed on Tuesday they were unable to reach an agreement with the Gunners, who they claimed tried to impose "absolutely unacceptable sporting and financial conditions" on any extension.
Arsenal insist they were willing for Saliba to extend his stay, but they wanted him to be on a specific training schedule and to not lose out financially.
"Throughout our discussions with Saint-Etienne, our aim has been to protect the welfare of William Saliba as well as the interests of Arsenal Football Club, while honoring the terms of the loan," a statement read.
"Despite the loan ending on June 30, we were willing to find a way for William to play in the [French] cup final on July 24, despite having no contractual obligation to do so.
"As William is returning from injury, we asked that Saint-Etienne follow a clear training plan with William in close collaboration with us, to ensure he is fully fit for the start of next season.
"To our surprise we were unable to reach agreement to this plan which was proposed by our medical experts, and we are simply not prepared to risk the welfare of an Arsenal player.
"While it was not our primary concern, and ultimately not relevant as our training plan was not accepted, we also expected not to be financially disadvantaged by extending the loan. This was also not acceptable to Saint-Etienne.
"We know this is a disappointment for William, but he understands we are working to protect his long-term interests and those of Arsenal."