The 39-year-old actress had filed a police complaint on June 12 night alleging she was molested by Wadia (44) at Wankhede stadium on May 30 when an IPL match was played between Kings XI Punjab and Chennai Super Kings, a charge the industrialist has denied as "false and baseless".
Zinta, according to her lawyer, is away in Los Angeles.
Meanwhile, a personal secretary to industrialist Nusli Wadia, Ness' father, who had claimed to have received threatening calls and a text message from fugitive gangster Ravi Pujari, asking the Wadias to 'keep off' Zinta "or their business will be in trouble", has identified Pujari's voice.
"The secretary was called to the anti-extortion cell last evening to see if she recognises voices from our voice bank. She recognised Pujari's voice as very similar to that of the person who made the threat calls," an officer privy to the investigation told PTI.
Two personal secretaries to Nusli Wadia were said to have received five calls and a threatening text message from Pujari on Monday following which an FIR was registered and case handed over to the anti-extortion cell of the crime branch for probe.
The officer said two separate investigations are now in progress in connection with the matter involving Zinta and and the Wadias.
"While Marine Drive police is probing the case of alleged abuse and molestation filed by Zinta, the anti-extortion cell of crime branch is investigating the one related to the threat calls made by Pujari," he said.
Police are trying to ascertain how the gangster, believed to be operating from Australia and south Asia, got hold of a phone whose number was traced to Iran, and how he got to know of the cell phone numbers of Wadia's secretaries.
Police Commissioner Rakesh Maria had said on Wednesday the calls received by Wadia's secretaries were "supposedly" made from Iran.
Following the threat calls and a text message from the underworld don, Mumbai police had on Wednesday deployed an armed contingent outside the Wadias' corporate office Wadia International Centre at Lower Parel.