Transport Secretary Philip Hammond said he wanted the air regulators to have new powers after the airport ground to a halt during the big freeze last week, ruining the holidays of tens of thousands of people.
A spokesman for BAA said: "We will of course play a full part in the Government's discussions about this year's weather disruption and will make public the findings of our own independent investigation.
"We welcome legislation designed to improve the experience for passengers at the UK's airports."
Mr Hammond told The Sunday Times it was unacceptable that BAA, which runs Britain's busiest airport, faced no punishment from the Civil Aviation Authority (CAA) under the current regime.
He said: "There should be an economic penalty for service failure. Greater weight needs to be given to performance and passenger satisfaction."
Ministers are considering a new airport economic regulation Bill, which would give more powers to impose fines for a wide range of service failures.
Under the existing system, fines can be imposed by the CAA for failures like passenger queues at security and cleanliness. The maximum total penalty is said to be 7 per cent of airport charges, resulting in a potential sum of 63 m.
BAA chief executive Colin Matthews announced that he would
forgo his annual bonus after last week's extended disruption at Heathrow.