The Bosnia international spent six years at Schalke before joining the Gunners in 2017.
Sky Sports Germany says discussions have already begun between the two clubs.
The Bundesliga outfit would be prepared to pay for half of Kolasinac's wages for the 2020/21 season.
Kolasinac is prepared to return to his native Germany for 'private reasons'.
Along with Mesut Ozil, the 27-year-old was a victim of an attempted carjacking in London in July 2019.
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