The France star was ruled out for up to seven weeks last month due to a hamstring injury, although there had been talk that he could be ready for the second leg with Monaco on April 22.
However, ahead of Tuesday's first leg in Turin, Allegri explained he was likely to have to do without Pogba for both games.
"It's pretty much impossible that Paul Pogba will be fit for the second leg," he said.
"[Andrea] Barzagli and [Andrea] Pirlo are in good shape, as are [Carlos] Tevez and [Gianluigi] Buffon, who are both fully recovered from their injuries.
"Tevez is having an extraordinary year. He must maintain his rich vein of form right until the last game.
"It's unlikely we'll see Pirlo and Barzagli in the same side tomorrow. It will either be one or the other."
Juve swept Borussia Dortmund aside in the last 16 and will be favourites to progress against Monaco, despite Leonardo Jardim's resolute defence.
"Without the same intensity and mentality we had in Dortmund, it will be difficult," Allegri added.
"I see the two games against Monaco as much more complicated because a team that concedes fewer goals makes games more difficult - you get the urge to hit back and allow more space, which we should not do.
"Dortmund are more offensive whereas Monaco are the opposite. We will have to have the patience to know how to deal with that."
