A government spokesman told the BBC the move was proposed by the Hindu Religious Affairs ministry, and said most moderate Hindu groups support it.
Some Hindus sacrifice goats, buffalo calves and chickens at temples as an offering to their deities.
But the practice has attracted years of protests in Buddhist-majority Sri Lanka, where critics call it inhumane.
Animals sacrificed at Hindu and Muslim religious festivals are often left to bleed to death, which angers animal rights activists and some Buddhist groups.
Many practicing Hindus choose not to sacrifice animals – but those who do have argued that the ban would impinge on their religious freedoms. They say such sacrifices are an ancient part of their faith that must be allowed to continue.
It appears the law would not cover animal sacrifice by Muslims, who are the third-biggest religious group in Sri Lanka.
Sri Lanka has experienced deadly religious violence in recent years, including anti-Muslim riots that killed three people in March. Nearly 450 Muslim-owned homes and shops were damaged.