Speaking to the Evening Standard, Cech said that Leno's arrival does not rule out an extension to his current contract.
"I'm in the last year of the contract so I guess it depends on my performances, the way I play and the way I stay fit throughout the season. Then we'll see what happens next," the stopper said.
"When you bring players in you do that to improve the squad and to make it competitive and Bernd is here, trains every day and tries to get his spot which keeps everyone in the goalkeeping group on their toes including me, obviously. I have to work hard not only to make sure the manager picks me for the weekend but as well that he sticks with me.
"The goalkeeper situation is complicated as only one can play so the competition is bigger and at the moment I've been playing and I try to do my best and hope the manager is happy with my performances. I've always had great goalkeepers — David Ospina was great as was Carlo Cudicini and Hilario — behind me who pushed me all my career so I have to make sure I'm ready."
Leno is expected to start in Arsenal's opening Europa League tie against Vorskla Poltava on Thursday.