The 21-year-old only signed for the Swiss champions last year, but has quickly emerged as one of their star performers.
His impressive performances have seen interest in his signature spike of late, with the Gunners thought to be keen.
Arsene Wenger is believed to be looking into the possibility of drafting in a new centre-back this winter after addressing his attacking concerns with a summer move for Mesut Ozil.
Italian champions Juventus are also interested, but fierce competition for a starting berth in his desired position may force Schar to opt against a move to the Italian giants.
His fine domestic displays have led to international recognition, and Basel sporting director Rudi Zbinden is thrilled with his player’s quick rise to prominence.
“We bought him from Wil in 2012 and many wondered who he was,” Zbinden said.
“Now he is a Swiss international and a regular in Ottmar Hitzfeld’s team.”
Basel are keen to keep Schar, but are aware that a big offer from a top club may be hard to reject.
The defender is contracted until 2015, but the Swiss side have the option to extend this by one year.
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