Gabriel, 25, injured an ankle against Manchester City, leaving them short of defenders for their Premier League opener against Liverpool on Sunday.
Per Mertesacker is out for five months with knee trouble and Laurent Koscielny only returned to training on Monday.
The Gunners are working on a deal to sign Mustafi, 24.
Mustafi, part of the Germany squad that reached the semi-finals of Euro 2016, began his career at Everton but made only one senior appearance for the Toffees, as a substitute in a Europa League match in December 2009.
He joined Sampdoria in 2012 and played 44 league matches for the Italians before moving to Valencia two years later.
Arsenal have made just the one defensive signing this summer - England Under-21 international Rob Holding from Bolton for a fee believed to be about £2m.
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Arsenal defender Gabriel has been ruled out for six to eight weeks, increasing the likelihood of a bid for Valencia centre-back Shkodran Mustafi.