The 41-year-old tennis champion has reportedly told the police that Mr Sharma threatened him in a court earlier this year.
He alleges that Mr Sharma is in a relationship with his estranged partner Rhea Pillai, and when he tried to show documentary evidence in court, the cricketer threatened him.
Mr Paes is battling a case filed by Ms Pillai, who has accused him of domestic violence and harassment. They have been fighting for the custody of their eight-year-old daughter.
Ms Pillai has accused Mr Paes’ father Vece Paes, of preventing her and her daughter from entering their Mumbai home.