In a letter to Modi, Swamy said India had signed a treaty on transfer of sentenced prisoners with Sri Lanka and invoking its provisions, the five fishermen could be brought back and allowed to stay in a prison in India pending their appeal.
He said, as per provisions of the treaty, the fishermen could be allowed to seek "legal remedies" in Indian courts.
The five fishermen, all hailing from Tamil Nadu, were apprehended in 2011 by the Sri Lankan Navy and are among a group of eight people sentenced to death by the high court in Colombo for alleged drug trafficking.
The Ministry of External Affairs had yesterday said that India's High Commission in Colombo will appeal against the verdict in a higher court.
Sri Lanka on Thursday, Oct 30, gave death penalty to five Indian fishermen who were arrested for allegedly smuggling drugs in the country.
MEA's Syed Akbaruddin said that they will take up the matter diligently and that the Indian high commission is pursuing the issue about the capital punishment with Sri Lanka.
India has been tracking the case since 2011 when the fishermen were arrested, said Akbaruddin. The Indian High Commission in Sri Lanka has been assisting the fishermen with legal aid. "We feel the fishermen are not guilty. We will follow the legal process and will do our best to get them back to India," he said.
The arrest of Indian fishermen who stray into Lankan waters has long been an issue in Tamil Nadu. Protest has broken out in Rameshwaram after the death penalty decision was announced.
The fishermen can appeal against the verdict by November 14, 2014.