In a 23-page motion filed in the Court of Appeals here, Gupta's lawyers asked the court for "an order staying his surrender date and continuing bail pending further appellate review".
Gupta, who had lost his appeal to overturn his conviction on insider trading charges, was ordered in April to surrender and begin his two-year prison sentence on June 17.
In seeking an order to stay his surrender date, 65-year-old Gupta is prepared to file a petition for certiorari on an expedited basis, the motion said.
Gupta had in April petitioned that a three-judge panel, which upheld his conviction and two-year prison sentence on insider trading charges, should reconsider its decision and the appeals court rehear the case, arguing that "critical evidence" in his favour was excluded at trial.
They said he presents no risk of flight or danger to the community and has abided by all conditions of release set by the district court.
"The certiorari petition that he plans to file if his rehearing petition is denied will raise at least two substantial questions, as detailed below. If either of those issues is decided in Gupta's favour, a new trial will be required. If bail is not continued, Gupta may serve half of his two-year sentence before the Supreme Court decides his case," they said.