Rossoneri fans have been rocked by the news that their most prolific striker is on the verge of joining Paris Saint-Germain, just days after their defensive linchpin Thiago Silva also sealed a move to the Parc des Princes.
Galliani, though, is promising to find a worthy replacement for the Swedish striker before the close of the summer transfer window.
"A champion will arrive in attack," he told Sky Sport24. "There is time until August 31."
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"I told the directors of Santos that I am not selling him and that he will remain at Milan," the Rossoneri chief explained.
Galliani also ruled out the possibility of a late attempt to hijack Roma's bid to bring Mattia Destro to the Stadio Olimpico, even though the Monza native admitted to having met with Genoa president Enrico Preziosi on Tuesday.
However, the chief executive explained that while he gave Walter Sabatini the fright of his life by answering Preziosi's phone during the sit-down, he quickly put the Giallorossi director at ease.
"When he heard who responded, he was terrified," Galliani laughed. "But then I told him that as far as we're concerned, there are no problems with Destro [going] to Roma."
Goal.com has already revealed that Milan are considering replacing Ibrahimovic with Manchester City striker Edin Dzeko.