And councillors have been speaking to the Sri Lankan High Commission about the details of how to arrange the scheme, which will give the city a unique five-year arrangement with the town.
Nearly 17,000 people were killed in the region around Galle when the tidal wave struck on Boxing Day, and a million were made homeless.
It was one of the worst affected areas in the country, where 38,000 are reported dead so far.
One of the British people to die in Galle was Britain's youngest-known casualty.
Two-month-old Charlie Smith died in the arms of his father Richard.
Last night Liverpool's executive member for housing and social care, Cllr Flo Clucas, said the move would help boost fund-raising in the city.
She said: "A lot of people from the region have come to settle in Liverpool in the past - particularly doctors.
"And the people of Galle have a lot in common with the people of Liverpool. Both cities are ports, with strong maritime and fishing traditions.