"Gupta filed a complaint and alleged that an unknown caller threatened to eliminate him. We are examining the complaint," Mr Singh said.
In the meantime, Mr Gupta has been provided security by the police.
Honeypreet, whose real name is Priyanka Taneja, and Mr Gupta, the grandson of former Gharaunda lawmaker Rulia Ram Gupta, got married in 1999 and filed for a divorce in 2011.
Last week, Mr Gupta alleged that the father-daughter relationship is a sham and claimed to have seen the two in a compromising position in the Ram Rahim's 'gufa', his private accommodation inside the sprawling Dera headquarters in Sirsa.
"Which father makes his daughter sleep on his bed? She never slept with me. Every night, she was with him (Ram Rahim). He never allowed Honeypreet to come to me," Mr Gupta told the media in Chandigarh.
He added that he fears for his life after speaking against the Dera head.
Honeypreet Insan, who has been absconding since Dera chief's conviction for raping two of his followers by a Panchkula court on August 25, was last seen with Ram Rahim in a special chopper that took him to a Rohtak jail.
She has been charged with conspiracy to help Ram Rahim escape. She has also been accused of sedition and inciting violence in which over 40 were killed in Panchkula and other cities in Haryana and Punjab.
Different state police including Haryana, Rajasthan, Punjab, Bihar and UP have launched search ops to trace her. Her photographs were pasted at police stations bordering Nepal in a bid to prevent her escape to the neighbouring country.
The Delhi High Court on Tuesday dismissed her transit anticipatory bail plea saying that she has been evading arrest and hence was not entitled to any discretionary relief.