Tamil Tiger leader Velupillai Prabhakaran, his intelligence chief Pottu Amman and rebel women's wing leader Akila were wanted in India for planning the 1991 assassination of Gandhi in the southern Indian state of Tamil Nadu.
Akila's name was dropped after she was killed by the Sri Lankan army in 1995, while on Monday defence officials announced Prabhakaran and Ammam were killed while trying to escape advancing government troops.
"The agency will contact the Sri Lankan authorities, through the Indian foreign ministry, for authentication of Prabhakaran's death," a senior official from India's Central Bureau of Investigations (CBI).
"We also want an authentication of Pottu Amman's death," the official added.
"If we get official authentication then the cases against Amman and Prabhakaran will also be closed," said the official.
India says the Tamil Tigers assassinated Gandhi in retaliation for his decision to send troops into Sri Lanka in 1987 in a peace-keeping operation that en