No a Private Investigator cannot legally tap your phone and listen into your conversations as that would be illegal and could get the private investigator charged with illegal wiretapping.
Private Investigators are not usually law enforcement and only law enforcement can legally wiretap someone's phone and listen to their conversations without the persons permission if they have a court ordered warrant signed by a judge.
The private investigator unless they were law enforcement would not be able to obtain a warrant for wiretapping your phone and if they did wiretap your phone that would get the private investigator into trouble.