The Gunners signed the Germany international in a £22m deal from Bundesliga side Bayer Leverkusen in the summer transfer window.
Leno has been signed to provide current number one Cech and his understudy David Ospina with competition for a starting spot.
However, Emery opted to stick with Cech in goal for the visit of the defending champions in their Premier League opener on Sunday.
Cech struggled in their 2-0 loss to Manchester City at The Emirates following goals from Raheem Sterling and Bernardo Silva.
Former Chelsea FC striker Sutton was bemused by Emery’s decision to start with Cech ahead of Leno.
“It was a big call to start Cech over Leno,” Sutton told BBC Radio 5 Live.
“They spent £22m on Leno and he sits on the bench. Cech didn’t have a good season last season.”
Arsenal have signed Juventus defender Stephan Lichtsteiner, Bayer Leverkusen goalkeeper Bernd Leno, Sampdoria midfielder Lucas Torreira, Lorient teenager Matteo Guendouzi and Borussia Dortmund centre-half Sokratis Papastathopoulos in the summer.
The Gunners haven’t won the Premier League title since 2003-04 under Emery’s predecessor Wenger.
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