The Arsenal boss has come under increasing pressure as his side faltered in the Premier League title race and exited the Champions League and FA Cup.
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And recent weeks, some fans have taken banners to matches calling for the Frenchman to leave.
Last month Henry, the club’s all-time leading goalscorer, completed his Uefa 'A' coaching badges which means he can become a manager below Premier League level or at a youth academy.
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But Wright feels the former France striker should be brought in now.
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“Thierry has got his badges, jump in, jump in,” Wright said.
“If you can’t get a Pep, which we can’t - Arsenal fans wouldn’t want Mourinho for whatever reason - if Thierry is ready to go and he can get the backroom staff, get it done.”
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