The first call was received by the Police Control Room on February 16 followed by another call the next day.
It is not confirmed whether there is one or more than one person involved in the threat call as the anonymous caller claimed to have overheard some persons who were plotting to harm the Bollywood actor.
The calls were soon traced to PCOs in south Mumbai's Marine Lines and suburban Malad.
Though the police have not yet taken cognizance of the matter or lodged any complaint, they are attempting to trace out the caller by checking CCTVs installed in those areas for further investigations, the official said.