Kossounou signed permanently for Atalanta last summer after spending the previous season on-loan with La Dea from Bayer Leverkusen.
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Africa Foot says Newcastle are interested in signing the 25-year-old, with intermediaries stating he could be available this summer for €25m.
Atalanta paid Bayer €20m to sign Kossounou at the beginning of the season.
The Ivory Coast international, 25, has a deal with Atalanta to 2029.