The corporation took over the cost from the Government of providing free TV licences for over-75s as part of its charter renewal negotiations.
The move is being phased in from 2018-19 with sole responsibility from 2020, when it is estimated to cost the broadcaster around £725 million.
BBC director general Lord Hall told the Digital, Culture, Media and Sport Committee: “The concession, as it’s currently formulated, comes to an end in June 2020. That was part of the last licence fee settlement…
“We, the board, have got to decide what to replace it with,” he said.
“We have got to be mindful … We know that those over 65 or over 75 consume many, many more BBC services than others… There is real hardship among some or many of those over 75 too.”
Pressed on whether the free licence fee for over-75s would be replaced, he told MPs: “It could be the same. The board could say, we will just continue with it as it is. It could be reformed. There’s a whole load of options.
“We are just not in a position to say what the right option will be. We have got to have a public consultation about what we do. “
He added: “We will make a decision at some point in the autumn or winter.”
A BBC spokesman said it was obliged to consult on what the policy would be from 2020 as part of charter renewal.
Caroline Abrahams, charity director at Age UK, said: “Increasing numbers of older people who live alone say their main form of companionship is their TV and for many others, especially those who are housebound, TV is a precious window onto the world.
“Anything that makes it harder for older people like these to enjoy watching TV would be a source of great concern to Age UK.”
The corporation is reportedly set to cut back its online services in an attempt to make its content easier to find as it looks to fight competition from US streaming services.
The BBC Earth and BBC Arts sections of the website are expected to be removed and there will be fewer features as well as less of a focus on celebrity gossip.
Instead, the corporation will focus on eight key areas: iPlayer, news, music and spoken word, weather, sport, children’s content, BBC Bitesize and the bbc.co.uk home page.
These areas are said to be responsible for more than 90 per cent of the BBC’s online audience.
The reported cull of services comes as the corporation attempts to overcome the challenge posed by the likes of YouTube and Netflix.