The new Europa League winners made an attempt for James last year, but found Brum's 10m valuation too rich.
La Gazzetta dello Sport says La Dea are ready to try again, encouraged by Birmingham's relegation from the Championship.
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Wales international James, 19, is set to attract a new bid from Atalanta and may push to leave given the prospect of League One football next season.
There is hope inside Atalanta that Birmingham will reduce their price for the youngster.