The 34-year-old Clarke, one of the best batsmen of his generation, presided over a series-losing defeat in the fourth Test at Nottingham's Trent Bridge ground on Saturday.
England won the fourth test by an innings and 78 runs, which saw them take an unbeatable 3-1 lead in the five-match Ashes campaign.
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The Sydney Daily Telegraph, the paper for which Clarke writes a column, said the star batsman would retire at the end of the Ashes even though only last week the Australia captain made clear his determination to continue his career.
Clarke, plagued by a longstanding back problem and more recent hamstring trouble, is in a desperate run of form with the bat, having reached 25 just six times in his last 30 Test innings.
He's the first Australian in more than a century to lose four successive Ashes series in England.
Were Clarke to stand down, heir apparent Steven Smith would likely become Australia's captain for their next Test series in Bangladesh.
Clarke has made 28 Test centuries, one short of Australia batting great Donald Bradman's tally, in his 114-match career.
There has been no official confirmation from either Cricket Australia or Clarke himself regarding his future plans, but the situation should be clarified when the captain carries out his usual post-match media duties at Trent Bridge.
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