Dutt's plea will be heard on Tuesday, reports said.
The Supreme Court on Mar 21 sentenced for five years Dutt to jail for illegal arms possession during the Mumbai bombings that had killed 257 people in 1993 in the nation's financial hub.
Amid a clamour for his pardon, Dutt on Mar 28 said he would not seek any pardon and would surrender before the law of the land and go to jail.
Dutt is due to surrender on Apr 18.
Dutt, who is the son of late legendary actor couple Nargis Dutt and Sunil Dutt, was accused of illegal possession of arms as lethal as an AK-56 rifle. He was, however, acquitted of graver charges under TADA or the Terrorist and Disruptive Activities (Prevention) Act.
On March 12, 1993, twelve coordinated blasts in Bombay Stock Exchange, Air India Building at Nariman Point and hotels Sea Rock and Juhu Centaur resulted in death of at least 257 people and injury to more than 700.
It was alleged that the blasts were the instruments to avenge the demolition of the Babri mosque in Ayodhya in December 1992 and were allegedly conspired by underworld don Dawood Ibrahim (believed to be hiding in Pakistan now) and two other terrorists-Tiger Memon and his brother Yakub Memon.