Defence Ministry Secretary Karunasena Hettiarachchi said that a licensing system was being explored.
"We have not finalised it. It is a very sensitive issue for both sides," Sunday Times quoted him as saying.
Technical proposals will be drawn up and submitted to the Indian Government through diplomatic channels, Hettiarachchi said, declining to give further details.
Yet the proposal which came from the Indian side is likely to face strong opposition the paper says.
The frequent arrest of Indian fishermen by Sri Lankan navy remained unresolved despite high level talks since 2014.
Sri Lanka accuses Indian fishermen of straying into its territorial waters, while the latter maintain they are only fishing in their traditional areas, especially around Katchatheevu, an islet ceded to Colombo in 1974.