Allegri assumed the reins at the Serie A champions after Antonio Conte departed to coach Italy and has led to club to the top of the table having suffered just one defeat in his opening 11 league matches in charge.
However, this season could have been very different for the former Milan boss had negotiations with Lazio to take over from Edy Reja been more productive.
"This summer I spoke with Lazio," he said ahead of Juve's clash with Lazio on Saturday. "I spoke with president [Claudio] Lotito, but we didn't find an agreement and didn't do anything. Then fortunately I arrived at Juventus.
"Lazio are a very good team. Firstly, they're well-coached, well organised and a very physical team.
"They're coming off the back of a defeat [to Empoli], they're smarting from that and will try to make things difficult for us.
"They're a team which can aim for third place, so it'll be a very difficult game for us."
Juve have had to endure a torrid time with injuries during the early stages of the campaign, but Allegri will have Andrea Pirlo at his disposal for this weekend's trip to Rome.
"Pirlo is training with the team," he added. "He's available and can play tomorrow night.
"As for the other injured players, [Patrice] Evra has almost recovered and, after Sunday, he will return to the squad, then he or [Kwadwo] Asamoah will play on Wednesday [away to Malmo in the UEFA Champions League].
"[Martin] Caceres we hope to have back after the Torino game [November 30], [Angelo] Ogbonna should be back with the team this week.
"[Andrea] Barzagli is here, even though he's not training with the team, and [Arturo] Vidal came back [from international duty] last night. He's fine, and he's available.
"Romulo has an ongoing groin injury, there are days when it's better and days when it's worse.
"We'll evaluate him today and see whether he'll be available for Saturday's game against Lazio."
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