Cassano fell ill following the Italian champions’ return from Rome on Saturday night after their 3-2 victory over Roma in Serie A and has been in the hospital since.
The exact nature of the Italy international’s problem is yet to be confirmed by Milan, which has, however, dismissed suggestions that he suffered a stroke.
The 29-year-old will miss the Rossoneri’s Champions League Group H clash against BATE Borisov in Minsk on Tuesday, but Zambrotta claims that Cassano is recovering well.
“We know that the situation in under control,” he is quoted as saying on Milan’s official website. “That’s what we know thanks to SMS and a few telephone calls.
“Personally, I sent him a message and he seems fine. Our thoughts are with Antonio not only as a player but also as the man we know, as a teammate."
Focusing on Milan's game against BATE, Zambrotta warned that his side cannot afford to be complacent against the Belarusian champions.
“We can’t take anything for granted as they’re at home and they’ll want a result,” said the Italian. “We want to get the top spot in the group.”
Milan is the current leader of Group H, level on seven points with Barcelona, which is second in the standings due to an inferior head-to-head record, and will visit Viktoria Plzen on Tuesday.