McGrath's bold claim comes after he predicted a 5-0 whitewash to Australia in the last Ashes series, only for England to win 2-1 and claim the trophy for the first time in 18 years.
He also nominated the then England captain Michael Vaughan as his bunny ahead of the last Ashes series -- only for McGrath to miss most of the campaign through injury and Vaughan to play a major role in his side's success.
Undeterred, McGrath again backed his abilities as a fortune teller Tuesday when asked which batsman he would dominate this time around.
"There's the young fellow Cook who's done well so far, he's one of many," McGrath told commercial radio in Sydney.
"There's no use naming one, these days you name two or three.
"They've captained Strauss at the moment, you always name the captain."
McGrath, 36, Test cricket's most successful fast bowler with 542 wickets, said he was feeling sharp and fit after a six-month layoff to help his wife Jane overcome breast cancer.
"The body feels good, just running in to bowl, so that was very good to get onto the outdoor nets," he said.
"It will take a little while to build it up but I'm probably in front of where I thought I would be."
Meanwhile, former Australian wicketkeeper and England academy chief Rodney Marsh urged the tourists to bring spinner Monty Panesar, backing him to make an impact on the series.
The Northamptonshire left-armer took five for 72 last week as England completed a crushing innings and 120 run victory in the second Test against Pakistan at Old Trafford, including the prize scalps of Inzamam ul-Haq, Mohammad Yousuf and Younis Khan.
While England coach Duncan Fletcher believes he must develop his fielding and batting before becoming the team's premier spinner, Marsh said Panesar had what it takes to claim top batsmen.
"Technically I think he's a very fine bowler," Marsh said.
"He's got as good an action as I reckon I've ever seen on a finger spinner. There's not much that can go wrong with him.
"They've got to bring him here," he added.
Marsh said the 24-year-old Panesar, the first Sikh to play for England, was also likely to hit it off with Australian fans after becoming a cult figure among the English public.
"The crowds will love him here -- one way or the other," he said.
"I'm sure the Australian batsmen will go after him, but they'll do that against any spinner."
South Australia, where Marsh is now high-performance director, said Tuesday it had written to English cricket chiefs offering to find places in grade cricket for any injured England players wanting a hit out Down Under ahead of the series.
England all-rounder Andrew Flintoff, spinner Ashley Giles and quick Simon Jones are all reportedly considering a stint in Australian domestic cricket.