Mr Matheson says ex-Army sniper Ray Tindall, 41, from Newton, Chester, and his compatriots are serving time in an Indian prison for a crime ‘they did not commit’.
The suggestion that should be put is that all six are deported, says Mr Matheson, which would see their return to the UK as free men.
Mr Tindall, who has a young daughter back home in Chester, and his five British colleagues were working aboard an anti-piracy ship when it was impounded by the Indian authorities in October 2013 after allegedly straying into their territorial waters.
Accused of illegally possessing weapons, the men, who have always protested their innocence, have been stranded in India ever since.
In January 2016, all 35 sailors and guards on the boat received five-year sentences and were ordered to pay 3,000 rupees (£30). An appeal is ongoing.
During Foreign Office questions, Mr Matheson told parliament: “It is more than three years since my constituent Ray Tindall and the other men of the ‘Chennai six’ were detained and subsequently imprisoned in India for a crime they did not commit.
“Will Ministers pick up the phone to their counterparts in India and suggest that the men are simply deported? The men do not want to be in India, and the Indians do not want them in India. It is an easy way out.”
Indian-born Alok Sharma MP, parliamentary under-secretary of state in the Foreign and Commonwealth Office, responded: “I know that the honourable gentleman is incredibly concerned for the welfare of his constituent, as we are for all the men.
“The prime minister, the foreign secretary and I have all raised the case in meetings with our counterparts. We are providing consular support, as the honourable gentleman knows, and my office has written to the families to say that I stand ready to meet them ahead of the verdict that is due.”
Mr Matheson MP, from Hoole, is convinced there has been a miscarriage of justice involving Ray, who was at one time known for running a Chester business called Faraly’s Fine Produce.
He says the Government encouraged a ‘softly, softly’ approach by allowing the Indian judicial system to go through its own processes but he has had enough.
The MP still intends to hold a fundraising event for his constituent in Town Hall Square.
“He went out there to earn money in order to build up his business. He lost more money than he was ever going to earn,” said Mr Matheson, who hopes to involve the Mission to Seafarers charity.