The former Czech Republic international has been first choice at the Emirates since his 2015 switch from Chelsea.
During Friday's Premier League opener against Leicester City, though, the shot-stopper struggled to keep out the visitors at the Emirates.
Cech ended up conceding three times, but he was saved by his team, who eventually won the game 4-3.
"I'm not sure that Cech will be number one at Arsenal come the end of season," Cascarino wrote in The Times. "The 35-year-old is nowhere near the level he was and rather than using his experience to compensate for fading ability he looks increasingly shaky in goal.
"He's playing on reputation but I'm not sure Ospina is good enough to replace him. If this becomes a problem Arsene Wenger may have to look at buying a goalkeeper in January."
Arsenal's next match is away against Stoke City on Saturday.