There is speculation that Kimmich may be sold by Bayern to raise funds for other signings.
Per Sky Sports Germany, the midfielder is considering a shock move to Arsenal.
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Kimmich can also play as a full back, but appears to prefer playing as a no.6 midfielder.
He has not enjoyed the best of spells since Thomas Tuchel took over as manager late last season.
Bayern would have to sell Kimmich this summer if they want to get a fee for him, as he is out of contract a year later.