Bayern see the France international as a replacement for Kingsley Coman, who is being sold to Saudi Pro League club Al-Nassr.
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L'Equipe says Bayern management are prioritising Nkunku as Coman's successor.
The German giants struck personal terms with Nkunku in January, but were turned off by Chelsea's €70m valuation at the time.
Bayern are now hoping Chelsea are more realistic with their asking price given Nkunku has been made available for sale this summer.
Driving the move is Bayern chief Max Eberl, who has been a fan of Nkunku since the Frenchman's time with RB Leipzig.