Inzaghi missed Milan's 1-0 derby win over city rivals Inter on Friday due to high temperature and the infection has developed to "full-blown tonsillitis", the magazine added.
Milan will face Barcelona in the first-leg of their UCL semi-final on Tuesday at the Giuseppe Meazza Stadium.
If confirmed, Inzaghi's absence comes as a huge blow Rossoneri coach Carlo Ancelotti who is relying heavily on the veteran striker along with Ukraine's Andrei Shevchenko in the front line.
Since his return from a long injury layoff, Inzaghi played a pivotal role in Milan's progression to the UCL semi-final, as he netted four goals in the last three games.
Alberto Gilardino, who is yet to score in the European competition, is likely to replace Inzaghi in Tuesday's highly-anticipated encounter.