Dutt had earlier skipped two court appearances in connection to the case.
Noorani has claimed damages up to Rs 2 crore from Dutt for walking out of his film 'Jaan ki Baazi' halfway in 2002.
He claimed that Dutt was paid Rs 50 lakh as signing amount.
The movie producer also alleged that he had received death threats from the underworld on behalf of Dutt, who was sentenced to five years in jail in the 1993 Mumbai bombings case last month.
The Supreme Court on Apr 17 gave four weeks more to Dutt to surrender before the law and go to jail to serve his term after his conviction in the 1993 Mumbai bomb blast case.
Dutt had requested for an additional six months' time to surrender.
He was to surrender by April 18 but he now has nearly a month more to complete his films and then go to jail.
The Supreme Court on Mar 21 announced its verdict on Dutt for illegal arms possession during the Mumbai bombings that had killed 257 people in 1993 in the nation's financial hub.
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.
