The Switzerland international is ready to sign a four-year contract with die Knappen but his current employers are demanding 6 million euros for his services
The Bundesliga outfit has identified the Switzerland winger as the ideal man to replace Michel Bastos, who spent last season in Gelksenkirchen on loan from Olympique Lyonnais before electing to join United Arab Emirates outfit Al Ain this summer.
Stocker has accepted Schalke's offer of a four-year contract worth 2 million euros per year but Basel's asking price of 6 million euros, plus bonuses, remains a major stumbling block.
Indeed, die Knappen have decided to wait until after their Champions League third qualifying round meeting with PAOK before deciding whether to meet the Swiss club's valuation of the 24-year-old.
Stocker, who starred for his country in Wednesday night's historic victory over Brazil, has established himself as one of the most exciting players in Switzerland since making his debut for Basel six years ago.
The versatile wide-man, who can play at left back as well as a winger, has notched three assists in just three games since the start of the new Swiss Super League season.