Italian media reported today Allegri was in the "hot seat"

AC Milan vice president Adriano Galliani said Massimiliano Allegri
position as coach of his team is still safe. He also denied the news
that the club is looking for a replacement candidate Allegri for next
season. Italian media had previously reported Allegri now was in the
"hot seat" following the failure of the Rossoneri in the Champions
League. Milan last week ran aground in the hands of Barcelona in the
quarter- finals. In the Coppa Italia, Milan also has been eliminated
in the semifinals. The only chance this season, earned his stay in
Serie A. Unfortunately, Milan last weekend just lost the top position.
"The position of Allegri is still safe. Do not listen to those who say
otherwise," said Galliani told Sky Sport Italia. Some of the names
reported to be a substitute candidates like Marco van Basten Allegri,
Marcello Lippi, Fabio Capello and Clarance Seedorf. However, Galliani
admitted his team have not been thinking of replacing Allegri. "I do
not understand why people doubt the coach, who has led us to the top
of the last two years, just because a small mistake," said Galliani.
Allegri has coached Milan since last season. In its inaugural season,
the former Cagliari coach was successful to give Milan the scudetto
and the Italian Super Cup.