The 33-year-old has been at the Emirates for nine years but is entering the final year of his contract.
BILD believes that Bundesliga runners-up Dortmund consider the France international as a serious option to strengthen their defence.
Arsenal are said to be willing to cash in on the centre-back now rather than lose him on a free transfer next summer.
Koscielny made just 17 Premier League appearances for the club during an injury-affected 2018/19 campaign that saw him ruled out with an achilles tendon injury until December.
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