Pedro left with multiple fractures after horrific Ospina collision
Ospina joined Arsenal for £3million in the summer of 2014 from Nice after the Colombian's stunning performances at the 2014 World Cup.
The 28-year-old shot-stopper has so far struggled to nail down a first-team spot at the Gunners, with Petr Cech favoured between the sticks.
He has hinted on a number of occasions this summer that he's keen to leave the Emirates, with Turkish outfit Fenerbahce said to be interested.
But Wenger admits he's convinced Ospina to stay put for the upcoming season, suggesting he has the chance to overtake Cech as his first-choice keeper.
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Arsene Wenger admits it was difficult to convince David Ospina to stay
It was not easy to convince Ospina to stay
Arsene Wenger
The Gunners manager said: "It was not easy to convince Ospina to stay, but he will play games and fight with Petr Cech to start.
"And anyway, we play other competitions. He wants to play in a World Cup year."
Arsenal kick start their Premier League campaign on Friday against Leicester, but Wenger admits a number of key players could miss out.
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David Ospina is behind Petr Cech in the pecking order at Arsenal
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Alexis Sanchez will not be in contention, while midfielders Aaron Ramsey and Mesut Ozil and defender Per Mertesacker are doubts.
Wenger added: "[Sanchez] has a little abdominal strain he did on Sunday morning. He had the scan two days ago. I don't know how long he is out.
"There are uncertainties over Aaron Ramsey, Mesut Ozil, Per Mertesacker."
