Vaughan has not played for England since last December because of a knee injury but had been targeting the fourth Test against Australia, starting in Melbourne on December 26.
However, he told a lunch at the National Sporting Club in London on Wednesday that he hoped to be playing cricket again in three weeks.
That would make him available for a two-day match with Western Australia on December 9-10 ahead of the third Test beginning in Perth on December 14.
Vaughan was quoted in Thursday's Independent as saying: "I hope to be playing cricket again in three weeks.
"The knee is coming on well and by that time I hope to be able to put a call in and say 'I'm available to play.'"
But he added: "Whether it takes two games, five games or a month to be match-fit is up to the selectors."
In 2005, Vaughan captained England to their first Ashes series win for 18 years. The first Test starts on November 23 in Brisbane.
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