Wilshere is out for three months after undergoing surgery on his left ankle to add to Arsenal's crippling injury list.
Wenger said: "He is very down. He is a football man who loves the game. On the other hand he is very strong as well and has learnt to deal with adversity from a very young age.
"He always comes out stronger and when I spoke with him he is already determined, it is already in his mind the final sprint to the season. He is a very strong boy.
"He's prepared and focused to come back and finish the season well. I think he will be back at the end of February, beginning of March and he will focus on coming back to rehab, having a strong rehab, and then I'm sure he will help us to do well until the end of the season."
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