According to police, a person claiming to be Ravi Pujari had called up the landline number of the office of Yash Raj Films located in suburban Oshiwara a number of times and demanded huge amount of money from Chopra.
The caller threatened that if the protection money was not paid the filmmaker would face "dire consequences", a senior police official said.
The filmmaker had written a letter to the city police informing them about the threat calls following which he had been provided adequate security.
Meanwhile, DCP (Operations) Rajkumar Vhatkar said, "Adequate security was provided to the filmmaker and we are trying to detect the caller."
He refused to comment on how much money had been demanded from the filmmaker.
Before Chopra, filmmaker Mahesh Bhatt and actress Ayesha Takia`s husband Farhan Azmi had also received similar threat calls allegedly from the Pujari gang.
Last week, police had arrested four members of Pujari gang for allegedly gunning down two site supervisors in separate incidents at construction sites.