The Daily Star says Wenger won't give up on the midfielder.
Cabaye appeared to suggest his new-found commitment extended only to the end of the current campaign.
"For Newcastle fans, football is their life and I want to say that I am going to give everything - as I have from my first day here - from today until the end of the season," he said.
"It is important I do that because Newcastle is my club and there is a World Cup at the end of the season, which I want to play in.
"It is very important to be right in my head and I am."
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