Kolasinac joined S04 in January on-loan to the end of the season without a permanent option.
BILD says S04 sporting director Peter Knäbel has held talks with Kolasinac and informed him they won't be pursuing an outright deal.
With a contract to 2022 with Arsenal, the fullback is set to be recalled by the Gunners.
With left-back a problem position for Arsenal, they're keen to count on Kolasinac for next season.
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