But they have persistently shunned the chance to regroup, turning down as much as 1 billion dollars to tour again in 2000.
However Benny Andersson and Bjorn Ulvaeus told The Times newspaper that an intimate one-off performance that could be screened around the world could be a possibility.
"Yeah, why not?" said Andersson, who now owns a farm where he breeds horses.
"I don't know if the girls sing anything any more," he added. "I know Frida was in the studio."
He added later: "It's not a bad idea, actually."
Ulvaeus said: "We could sing 'The Way Old Folks Do,'" in a reference to one of their "Super Trouper" album songs.
Observers have always thought too many barriers existed to the band reforming, including the reclusive lifestyle of the blonde female member Agnetha Faltskog.
Andersson and Ulvaeus have responded negatively in the past too. Two years ago Ulvaeus said: "We will never appear on stage again. There is no motivation to regroup. Money is not a factor and we would like people to remember us as we were -- young, exuberant, full of energy and ambition."
Lyngstad married a German prince and lives in the Swiss Alps. She is thought to be relatively amenable to a reunion, the newspaper said.
Ulvaeus and Andersson are currently promoting their musical "Kristina" which opens in London on April 14.
(Writing by Avril Ormsby; Editing by Steve Addison)