Tuchel has just led Bayern to the Bundesliga title after a dramatic last day triumph. But the former Chelsea manager was left upset after seeing chief exec Oliver Kahn and sporting director Hasan Salihamidzic sacked on Friday.
Hamann said, "When you treat people like this, you have to ask yourself: Do you want to work for this club?
"I don't think you can rule out Tuchel leaving soon too. But he'll leave of his own accord."
Hamann's fellow pundit, Erik Meijer, then added: "I think he'll have left the club by Monday."