The family of the girl is set to meet Mukherjee Jan 7.
"We are scheduled to meet the President Jan 7 and will place our demand for a CBI inquiry," the father said.
He said: "I want to request the CBI to carry out a thorough investigation ... so that I get mental peace. If there is no proper probe, we will go to the President with our grievance."
The teenage girl was gangraped twice in October in Madhyamgram in West Bengal
The girl was gangraped twice in October in Madhyamgram of West Bengal's North 24 Parganas district.
She died Tuesday at a government hospital where she was admitted with severe burn injuries Dec 23.
The police have slapped murder charges against two accused, now under custody, based on the girl's dying declaration the duo set her ablaze.
The father, a taxi driver hailing from Bihar, questioned the absence of forensic investigation following the burning incident.
He said, "It has been so many days but the forensic team is yet to visit the scene ... we do not have any kind of security. They (those who set her ablaze) were not quizzed ... no forensic tests were carried out ... that means they want the case to be closed."