The 23-year-old has less than six months left on his contract and is free to sign a pre-contract with another club.
During the January transfer window, Chelsea were rumoured to have made a move for the Bosnia international.
Arsenal's January-February form ranked over 10 years
Tue, February 7, 2017
How many points have Arsenal racked up in January and February over the last 10 years?
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Arsenal's January-February form ranked from best to worst since 2007
But Schalke sporting executive Christian Heidel said the Premier League leaders did not make an official offer.
However, German newspaper Bild say the Gunners are keen on Kolasinac.
Schalke defender Sead Kolasinac
Arsenal could be on the hunt for a left-back in the summer with Nacho Monreal’s dip in form and contract uncertainty surrounding Kieran Gibbs.
In November, Kolasinac said he would have to consider his family when deciding whether to move to England.
Chelsea were interested Sead Kolasinac
"Many say my style of play would fit well in England," he said.
"But if I move abroad, not only the club changes, but you leave your environment, need to build something new.
“It's a difficult step which has to be well-considered. The gut feeling decides, and I also need to talk to my family."