Deshmukh told the assembly that the police had taken note of the incident and a report would be tabled in the assembly soon. He, however, didn't set a timeframe for the submission of the report.
Earlier, the Maharashtra assembly witnessed uproarious scenes Thursday with the opposition asking the government to take immediate action against Salman for threatening Aishwarya for not performing in an event sponsored by an underworld don.
Referring to the explosive telephonic conversations between Salman and Aishwarya published by an English daily, opposition Bharatiya Janata Party (BJP) members demanded a high-level probe.
"If the transcripts are true, then it is really a very serious issue and the government must take action against the culprits," said senior BJP leader Gopinath Munde.
"In the tape, Salman has clearly admitted his links with the underworld and threatened a reputed actress like Aishwarya. He should be immediately arrested and his passport should be seized," he added.
"We want to know why the police didn't take any action in this case all this while despite recording the phone conversation in 2001."
Hindustan Times, which launched its Mumbai edition Thursday, published transcripts of phone conversations between Salman and Aishwarya that were recorded August 28-31, 2001.
According to the daily, Salman began calling up Aishwarya soon before her departure to the US on a 50-day tour.
During the conversion, he reportedly threatened Aishwarya with dire consequences if she didn't perform for underworld don Abu Salem's show. He also admitted his links with Dawood Ibrahim and Guru Satam.
Salman's lawyer Dipesh Mehta said that the tape had been fabricated to malign his client.
"This is not his (Salman's) voice. His image is being unnecessarily tarnished. There is no truth in whatever has been reported," said Mehta.
"If the tape was authentic, then the police would have taken action instead of sitting on it for the last four years."
Both Salman and Aishwarya were not available for comment.