25-year-old Azam played a knock of 157 against Australia A last week and is also ranked as the number-three batsman in the ICC ODI rankings.
The 44-year-old Ponting also hailed Josh Hazelwood and Pat Cummins for not leaking runs and being outstanding for a consistent period.
He is the latest great to be brought into the fold after Ricky Ponting joined the backroom staff at the one-day World Cup this year and Steve Waugh helped out during the Ashes series in England.
Smith has been in sensational form with the bat following his return to international cricket after serving a one-year ban for his role in the Sandpaper Gate fiasco.
Virat Kohli on Friday emulated former Australia skipper Ricky Ponting by equalling the record 19 hundreds as a Test captain.
Ponting said the efforts of Paine's side should be congratulated even though they didn't manage to win the coveted series.
Ponting, who has been a sounding board for coach Justin Langer in recent months, unsurprisingly nominated the in-form Steve Smith and Marnus Labuschagne as the other two.
Warner, 32, has all single-digit scores barring a 61 in the Leeds Test. He also got out to England pace spearhead Stuart Broad six times, including on a duck on three consecutive occasions.
Ponting, who is serving as Australia assistant coach, also narrated what went on with the team after Paine won the toss as the development took him in utter surprise.
Ponting also believes that Australia's win at Old Trafford proves that there is no such thing as momentum in cricket.
Smith re-wrote the history books with his 26th Test century and third Ashes double hundred as he batted for 513 minutes, and hit 24 fours and two sixes.
Kohli has struck 18 Test centuries as Indian skipper and needs just one more century to equal Australia's Ricky Ponting's tally of 19 Test tons as a skipper.
Archer first hit Smith on the forearm before send a hurling a bouncer flush on the prolific run scorer's neck while he was on 80.
Ponting believes that Warner needs to 'free himself' in the mind.
On Wednesday, Kohli scored his second consecutive century to help India beat West Indies by six wickets in the third and final ODI of the three-match rubber.