Pirlo has 116 caps and is widely regarded as one of the world's all-time great deep-lying playmakers.
But the 36-year-old's move from four-time consecutive Serie A champions Juventus to New York City FC has coincided with a dip in form and the 'orchestrator', as Pirlo is often known, has looked somewhat out of tune.
Pirlo looked far below his usual best during a 1-0 win over Malta last Thursday and, although he has Conte's backing, he was sidelined for Sunday's 1-0 win at home to Bulgaria which took Italy to he brink of booking their ticket for next summer's finals in France.
The back-to-back wins sent Italy top of Group H with a two-point cushion on Norway and they require just one point from their next two encounters – away to Azerbaijan and at home to Norway – to qualify for the European Championships.
The Euro 2016 finals will Pirlo's last international tournament, but his performance against Malta last week has prompted debate that even that could be a step too far.
“I think every player has to know when it's time to hang up his boots,” said Beppe Marotta. Coming from the CEO of Juventus, whom Pirlo helped lead to four 'scudetti' and the Champions League final last season, it must have been painful reading.
Marotta added: “I don't know if that moment has already come for him. It's a decision only he can make.”
Against Bulgaria, Roma's midfield general Daniele De Rossi stepped in for Pirlo in the middle of Italy's three-man midfield, flanked by Marco Verratti and Marco Parolo.
Italian sports media on Monday were quick to jump on the fact Verratti admitted he fared better playing alongside De Rossi than with Pirlo last week.
But the Paris Saint Germain star explained: “Maybe I played a little better tonight (Sunday), but that was because Bulgaria gave us more space than Malta did.”
De Rossi, a no-nonsense defensive midfielder with a history of indiscipline, fired Italy into a sixth-minute lead from the penalty spot after Antonio Candreva was fouled in the area.
But De Rossi's poor disciplinary record was blotted again when he was sent off 10 minutes after the restart for retaliating to a foul by Iliyan Mitsanski by kicking back at the striker. Mitsanski was also dismissed.
Conte's feelings on the incident were clear after the game when the coach, before walking briskly away from the interviewer, said curtly: “He shouldn't have done it.”
Indiscipline of the sort will not be welcome at next summer's finals, where Italy would be looking to make amends for their first-round exit from last summer's World Cup in Brazil.
And Conte, perhaps riled by Marotta's comments, continues to give Pirlo his backing.
“What disappoints me most is the lack of respect shown towards an immense player. He deserves more respect in every way,” Conte told Sky Sport after Sunday's win.
“Pirlo cannot be considered irreplaceable one day and the next ready for the scrap heap.”
Italy goalkeeper Gianluigi Buffon, 36, agreed.
“Every player knows when it's time to stop, but if you ask me Andrea still has plenty to offer,” said Buffon, who made his 150th appearance for Italy on Sunday.
“He could even become crucial for us, as he always has been when games really matter and the ball is zipping around the field.”
Italy face a potential banana skin on their next encounter, away to an Azerbaijan side that held Croatia to a scoreless draw at home last week before being held 2-2 by Malta on Sunday.
An Italian win at the Bakcell Arena in Baku next month should be enough to see them through before they host Norway, but Conte said it's not time to celebrate yet.
“We're not qualified yet, so that has to remain our main focus,” Conte added.
“Our group is the toughest of all. We have 18 points from eight games and we still aren't qualified. Anyone who thinks it is going to be easy has got it wrong.”