The Daily Star Sunday says both clubs were on the Basel centre-half's trail this summer before deciding to pursue other targets.
But Gunners boss Arsene Wenger is short of defenders and is weighing up a cut-price deal for the 22-year-old.
Schar is valued at £10m by Basel but is out of contract next summer and likely to be available for much less in January.
Spurs sporting director Franco Baldini watched him recently and the club also sent a scout to see him in action against Real Madrid this week with a view to a potential bid.
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