Lee said he was keen to return to the Melbourne Cricket Ground for the Boxing Day Test, where he took 5-47 in his Test debut eight years ago.
"Time has flown by so quickly and there are some absolutely great memories playing at the MCG, on a team basis and an individual basis," Lee said.
"We have always said that playing against England in the Ashes is where it's at, but I also think now playing against India is one of our greatest challenges as far as Test match cricket goes."
When the Border-Gavaskar Trophy was last contested in Australia in 2003-4, Australia struggled without the injured Glenn McGrath and suspended Shane Warne and the four-Test series was drawn 1-1.
Lee led the bowling attack during the recent series win against Sri Lanka, taking 16 wickets at 16 runs each and ultimately being named player of the series.
"I'm personally really, really happy with the way that I'm playing and I'm happy with the way the team's going," said Lee, who has never played a Test in India but is hugely popular in the subcontinent.
India have recently settled on former South African batsman Gary Kirsten as their next coach after Australian Greg Chappell resigned following the country's early exit from the World Cup in March.
Kirsten will join the team on December 3, just two weeks before they leave for Australia to play the four Tests and a triangular one-day series also featuring Sri Lanka.
Meanwhile, Australia's injury woes continue to mount with Test opener Matthew Hayden suffering a knee injury, which forced him out of a domestic match Wednesday.
Fellow opener Phil Jaques has been laid low with the mumps, while batsman Michael Clarke missed a one-day domestic match Wednesday due to a hamstring complaint and all-rounder Andrew Symonds has a foot problem.
But the most serious injury faces spin bowler Stuart MacGill, who struggled with hand numbness while bowling against Sri Lanka in Hobart last week, and may also still require knee surgery that could rule him out of the India series.
"We still don't know what to do," his manager Leo Karis said.
"He's assessing his options and whether that option is A, B, C or D, his main focus is playing cricket pain-free and that's up to him to see how he does that."
The Indian team arrives in Australia in mid-December.