The former Blues boss has experience of working with the Croatian midfielder during his stint at the west London club.
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Kovacic has made 217 appearances for Chelsea since he initially signed on loan from Real Madrid in 2018.
He made the move permanent the following year and his contract will expire next summer, with Tuchel potentially interested in a transfer.
As reported by Christian Falk, the Bayern manager is 'dreaming' of a player like Kovacic.
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The 28-year-old is also said to speak 'perfect' German, which will likely come in handy should he move to the Bundesliga.
Kovacic made 67 appearances across six different competitions when Tuchel was the Chelsea manager.
He is therefore a proven and reliable asset, and a player who could make the difference for a struggling Tuchel next season.
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The German has endured a mixed start to life at Bayern, winning just two of his first seven games in charge.
Bayern are now out of the Champions League and the German Cup, and have dropped to 2nd in the Bundesliga.
Their most recent result was a 3-1 defeat away at Mainz with club CEO Oliver Khan, sporting director Hasan Salihamidzic and chairman Herbert Hainer all seen visiting the dressing room afterwards.
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Bayern sit one point behind leaders and Tuchel's former club Borussia Dortmund with five games left to play.
If he is unable to guide them to their 11th consecutive league title, Tuchel could certainly have a rude awakening in his first season in charge.