Gupta, 63, was sentenced to two years in prison by US district judge Jed Rakoff on insider trading charges and was scheduled to begin his prison term on January 8.
Federal prosecutors have asked the appeals court to deny Gupta's request, saying the India-born Wall Street executive is a "flight risk" since he has strong personal and financial ties to his native country.
Rakoff had also denied Gupta's bid to remain free on bail pending appeal when he had sentenced the former McKinsey head last month but had said Gupta was not a risk of flight. Rakoff said he would recommend the federal prison in Otisville, New York for Gupta to the Federal Bureau of Prisons.
Gupta was convicted in June of passing confidential boardroom information about Goldman Sachs to his friend and business associate Raj Rajaratnam.