Allegri has overseen an unprecedented run of dominance for the Turin club since succeeding Conte in the job in the summer of 2014.
The coach is on course to win his fifth consecutive Serie A title this season, with Juve a massive 18 points clear of nearest rivals Napoli.
That would also mark Juventus' eighth straight Scudetto, extending what is already the most successful run in the club's history domestically.
Local dominance has not translated into continental success though, with Juventus last winning the Champions League in 1995-96, the season prior to Montero's arrival.
But if Allegri does decide to end his five-year association with the club, Montero believes they have what it takes to attract a top coaching name.
"Would I be surprised to see Conte or Zidane next season? Not at all. Juventus have reached a very high level and if they change their coaches, they will certainly take a top one," the Uruguayan explained to Goal.
"Zizou and Antonio are two winners, they know the environment very well, they are both important names."
Montero, who spent a total of nine seasons in Turin, added that he still backed Allegri for success, despite claims that a fresh face was needed to rejuvenate Juve's continental dreams.
“Is it difficult to follow the same coach for five years? No, I don’t think so. We had Marcello Lippi for a long time and the focus has always been very high, the strength of the club is very big, and Juve are a very powerful club," he said.
"Every day at Juventus they make you understand the importance of the club, the goals you need to achieve. You cannot go wrong. If you make a mistake, they immediately buy someone else in your place. It’s a matter of mentality."
Juve's Champions League campaign in 2018-19 hangs by a thread, as they look to overturn a 2-0 last-16 deficit to Atletico Madrid in Tuesday's second leg.
Montero, though, has no doubt that the Old Lady are capable of springing a memorable comeback.
“Yes, absolutely [Juve can turn it around]. Juventus are a top team," he added.
"Of course it wil be a very difficult game because Atletico are a very difficult opponent to beat, but Allegri is able to prepare his team in the right way. Juve have everything to find a special night.
"I really like Allegri, he always find the right solutions for these kind of matches."