The forward, who helped Italy claim the Euro 2020 trophy against England in the final at Wembley on Sunday, is a target for the German giants.
However, the new Bayern coach Nageslmann admits their chances of signing Chiesa are slim to none, as his parent club Fiorentina would demand a massive fee for the attacker.
"Yes, he's good but he's expensive, too," Nagelsmann told Bild.
When asked about a position change for Bayern winger Serge Gnabry, who could play as a right full back in certain games, Nageslmann added: "He's a top player, with incredible drive.
"I known him for a long time and I find him exceptional because he often goes for a one-on-one, he tries to shoot very fast.
"It's always about thinking: How do our opponents play? So it can be an option, but certainly not the solution for 34 game days.
"He is not a top-notch solution for this position. Serge's position is more central in front, on ten, in half space or on the wing, that's where he plays his best."
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