He has been at the German club since the start of the season on a loan deal.
And Bild suggests that he has grown fond of Gelsenkirchen as he looks to build his career.
His loan deal has no option to buy, so Schalke would have to negotiate a transfer fee.
They may even try to get him on another loan deal, but Everton would prefer to get a fee for the fullback.
Kenny has 26 games, one goal and three assists to his name this season.