After his side's pre-season victory over Boreham Wood on Saturday, Wenger said he would bring in a new keeper "for sure" and confirmed he was actively looking.
Ospina announced in May ahead of the World Cup that he would not renew his contract with OGC Nice, which runs until the end of the 2014/15 season.
The 25-year-old put in a stellar performance for his country in the tournament in Brazil, conceding the least amount of goals of any South American goalkeeper in the tournament.
Wenger is in need of back-up to regular No 1 Wojciech Szczesny after the Pole's compatriot Lukasz Fabianski left the Emirates to join Swansea City on a free transfer.
The Frenchman has already bolstered his playing squad this summer with the signing of Chile forward Alexis Sanchez, from Barcelona, and also brought in Newcastle United right-back Mathieu Debuchy earlier in the week - splashing out at least £42m in the process for the pair.