Wilshere limped off during Arsenal's 0-0 draw at Chelsea on Wednesday night with a sprained ankle and Wenger said afterwards that he expected him to miss this Sunday's trip to the Vitality Stadium.
Speaking to reporters on Friday, Wenger said: 'From Wednesday night, Jack was injured but we had good news. "If it's me in charge or somebody else, you can only do what is best for the club".
"At the moment we have five big injuries and we're hoping to get some back".
Asked about Ozil's injury, Wenger added: 'It's his knee.
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Meanwhile the Cherries are looking to pull away from danger at the bottom of the Premier League table, as they now sit just one point and two places above the bottom three heading into this fixture.
Wenger will be able to call upon Wales worldwide Aaron Ramsey, however, as he returned to the squad after being ruled out for over a month. "We will have Ramsey back in the squad", Wenger confirmed. 'Koscielny next week, Kolasinac next week, Monreal, earliest next week as well.
However, striker Olivier Giroud will have to wait a little longer as he's still two weeks away from making his return from a hamstring injury that's kept him out for over a month. "Never. Why should I change?"
'The second game was not too bad as I was in a fantastic position with the media.