The Daily Star says Gunners No.1 Petr Cech has accepted the arrangement, as he appreciates the ability of the Colombian international and gets on very well with him.
Ospina, 28, was Arsenal's hero with an inspired display in the 1-1 draw against Paris Saint-Germain on Tuesday.
Wenger revealed after the match he had made a “rule" for the keepers this season and that is believed to include Ospina keeping his place for European games as long as he maintains his form.
Cech is expected to return for the Premier League trip to Hull on Saturday with Ospina back in goal for the EFL Cup tie away to Nottingham Forest next Tuesday.
"Petr's fine, it's everyone else that's surprised by it," said a source.