The two legends had been on multiple tours down under through their illustrious careers.
While for Kumble, much depends on how India start off in the Adelaide D/N pink-ball encounter, Dravid believes the team will need someone to do what Cheteshwar Pujara did on the last trip: bat for hours, grind the opposition bowlers down and allow India to post huge totals on the board.
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Both the legends were asked for their predictions for the series during a webinar organised by L&T Financial Services Mutual Fund's annual conclave 'The Winner's Circle' on Thursday (December 10)
Kumble said, "Since India is starting the Test series with a pink ball, that'll be the biggest challenge. If we can stay ahead in the first Test match then India has a great chance to repeat what they did in the last Australia tour."
"Although with [Steven] Smith and [David] Warner coming back [after their ball-tampering bans the last time] and then Virat [Kohli] missing the three Test matches will obviously be a big factor for India," he added. "But having said that, there's enough ability within the team, be it batting or bowling."
On the last trip, Pujara enjoyed a memorable series, similar to the one Dravid had during the 2003-04 tour. The unmoveable right-hander scored 521 runs, including hundreds in Adelaide, Melbourne and Sydney, as Kohli's men came out triumphant with a 2-1 series scoreline and became the first Asian Test side to conquer Australia.
"Who is going to be our Pujara from last time?" asked Dravid, who is now National Cricket Academy (NCA) head. "I'm saying [that because] Pujara scored 500-plus runs last time, [so] you [are] going to need one of your batsmen [to repeat that]."
"Either it is going to be Pujara himself - obviously it can't be Kohli because he is not going to be there for the whole [tour] - but you are going to need one of your batsmen at least in my opinion over the four Test matches to get you something like 500 runs."
"I do believe we have got a bowling attack that can take 20 wickets in those conditions. They will be challenging conditions: Australia will try and put out conditions which will support the quality of fast bowlers. So will we be able to match that?"
"I think we will be able to get 20 wickets over five days. [But] will we get a batsman who will get 500-plus runs for us in the series [or not] might define it; if we can get that, then we give ourselves a great chance. If one of Smith and Warner, who missed the last series, get that then they [Australia] probably will have the edge," he added.
It's the return of Steve Smith and David Warner, coinciding with Kohli, inarguably India's best batsman, going on paternity leave after the first Test, that both Kumble and Dravid agreed might just prove to be a decisive factor.
"The bowling - we probably match our fast bowling to their fast bowling," Kumble said. "The batting again matches, [but] I think we are ahead [of Australia]. So if we can get ahead in the pink-ball Test match - which obviously is Australia's strength: they've done really well in Adelaide whenever they have played a pink-ball Test; so if India can sort of get ahead against Australia in the first Test, then I will back India."
"But if that doesn't [happen], then it is going to be a tough ask without Virat as well in the next three [Tests]."
(Inputs from ESPNcricinfo)