The Brazil international has been out of action for just over a month with a niggling thigh problem and is expected to make his comeback against the Nerazzurri on Sunday evening
The Brazil international has been out of action since aggravating a thigh problem during the warm-up ahead of the March 24 clash with Roma but had been expected to return to action either against Siena last Sunday or against Atalanta on Wednesday night.
However, Allegri has now revealed that Thiago Silva's first game back is most likely to be against the Rossoneri's city rivals this Sunday.
"I don't think he will be at our disposal for the Atalanta game but I hope to have him back for the derby, which is much more important given what is at stake," the 44-year-old coach told reporters on Monday.
Meanwhile, Allegri insists that he can understand why the fit-again Mathieu Flamini lashed out at him over his ongoing exclusion from the Milan starting line-up.
The French midfielder claimed last week that he has fully recovered from the knee injury he suffered in pre-season training and that he has been left in the dark as to why he has not been welcomed back into the first team.
Allegri insisted that there has been no falling out with Flamini and expressed his sympathy for the former Arsenal man's current plight.
"I understand Flamini's outburst, as with anyone who is having to sit in the stands," the former Cagliari boss stated.
"But one has to make choices and I always try to field the best team. Of course, if you ask any player, they all think that they deserve to play."
The Rossoneri take on Atalanta on Wednesday needing a win to stay in the Scudetto race for at least one more matchday. They then meet city rivals Inter on Sunday at 20.45CET in the penultimate league game.