Vaughan, the 2005 Ashes-winning skipper, has made a strong recovery from knee surgery and proved his fitness in a practice match on Friday in Bowral, south of Sydney.
The England team has called a press conference with chairman of selectors David Graveney and Vaughan here on Sunday when he is expected to be named as skipper, the Daily Telegraph said on Friday.
Vaughan is expected to lead England in the Twenty20 match against Australia at the Sydney Cricket Ground on Tuesday and the ensuing one-day tri-series against Australia and New Zealand, beginning next Friday in Melbourne.
Vaughan has been out of international cricket since a recurrence of a long-term knee injury required more surgery through the northern summer.
His comeback plans intensified when he joined the English academy side in Perth last month, although he has struggled for runs.
Vaughan's form in one-day cricket has been a major concern since he replaced Nasser Hussain as skipper but the tourists are desperate to embrace his leadership, the newspaper said.
"I feel ready, mentally I am very fresh," Vaughan said earlier this week.
Vaughan's return completes a disastrous seven weeks for Flintoff, who will be remembered as only the second England captain ever to preside over a 0-5 Ashes wreckage, and the first in 86 years.
It will be the first major move of a comprehensive review into a disastrous campaign where the tourists went from Ashes heroes to whitewashed flops within 16 months.
Flintoff was unsure at his post-match press conference whether he would retain the top job.
"I enjoyed doing it and I couldn't ask any more of the lads. If I had the chance again of doing it, I'd jump at it," Flintoff said Friday.
"As captain, I think I've learned a lot throughout this trip.
"When you're making decisions out in the middle, you go with your gut feelings and do what you feel is right at the time and I stick by that."
Flintoff's Test performances were sub-par, but he denied the added burden of captaincy had weighed him down.
A sore ankle prevented him from being the bowling force he was in 2005, while his footwork when batting was sluggish until his 89 in the first innings in Sydney.
Flintoff finished the series with 254 runs at 28.22 with two half-centuries in 10 innings and 11 wickets at 43.73 off 137 overs.