Hamann has called for Tuchel to be dumped by Bayern ahead of next week's Champions League quarterfinal against Arsenal.
He told Sky Deutschland: "In my opinion, the management must now ask themselves if they want to enter the final phase of the Bundesliga and the Champions League with Thomas Tuchel as head coach. They have to think about whether to hire a new coach for the last weeks of the season.
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"There are many on the market. I think of Jos Mourinho. You can think what you want about Mourinho, but at Chelsea he was loved by the players.
"He is incredible, if you look at it from a professional perspective."