"I will talk to Prime Minister Narendra Modi and External Affairs Minister Sushma Swaraj on the issue," Vijayan said in the state assembly.
He was replying to a submission by Kerala Congress (B) MLA, K B Ganesh Kumar on the plight of the 27-year-old youth, Praveen, hailing from Pathanapuram in Kollam.
Praveen is lodged in a Kenyan prison along with another Indian sailor cadet Vikas Balwan from Haryana.
Vijayan said the field agency of Non-Resident Keralites Affairs - NORKA Roots - has written to the Indian High Commissioner in Kenya to inquire into the case.
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The youths have been in prison for about two years for no fault of theirs, Ganesh Kumar said and called on the chief minister to take up the issue with Modi when he visits Delhi.
The two, along with six Pakistani crew members, including captain of Iranian merchant vessel MV Amin Darya, were taken into custody by Kenyan security agencies at Mombasa port on suspicion of trafficking drugs in July 2014 after eight kg of heroin worth USD 12 million was recovered from the vessel.
Praveen's father, Prabhakaran Nair, an ex-serviceman, had to sell his property for getting a lawyer to fight his son's case in Kenya, Kumar said, adding, his mother also was bed-ridden after hearing of her son's plight.