The filing of the request with the 9th U.S. Circuit Court of Appeals means Baca will automatically avoid prison for a slightly longer amount of time. He had previously been scheduled to report to the federal Bureau of Prisons on Tuesday.
MORE: Former LA County Sheriff Lee Baca sentenced to 3 years in prison for obstruction
The ex-sheriff's surrender date has now been postponed until the 9th Circuit panel of judges responds - a process that could take several weeks.
"As the district court and the government acknowledged, Sheriff Baca, who is 75 years old and suffering from Alzheimer's disease, is not a danger to the community nor a flight risk," Baca's attorney, Nathan Hochman, said in a statement. "We have raised numerous such issues, from the district court's complete preclusion of Sheriff Baca's Alzheimer's expert to the district court's unjustified use of an anonymous jury.
"We look forward to the Ninth Circuit considering this motion," the statement said.
On Thursday, Baca had asked a lower court to allow him to remain free while his conviction moves through the appeals process. That request was rejected by a judge.
MORE: Audio recordings reveal alleged Baca lies
Baca was convicted in March of conspiracy, obstruction of justice and lying to investigators who were probing the L.A. County jail system he headed.
The Associated Press contributed to this report.