The Gunners will be without first-choice striker Jesus for up to three months after the Brazilian suffered a knee injury on World Cup duty.
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While there are suggestions Arsenal could sign a forward in January, with Joao Felix and Mykhailo Mudryk among the names mentioned, Zinchenko is not worried about their current options.
The former Manchester City defender admits Jesus will be a 'big miss' - but hailed the quality of England youth star Nketiah, who looks set to deputise when the Premier League returns on Boxing Day.
"We are all behind him [Jesus] and supporting him, of course it's a big miss for our team," Zinchenko told Sky Sports.
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"The impact of what he's doing for the club is amazing. I've known him for a while and he's a big warrior and I'm 100 per cent sure he will be much, much stronger.
"Since I came here, [Nketiah] has been amazing. Honestly, even watching him last season, I was surprised a lot because the ability and quality he has is incredible.
"He has an amazing potential and future for sure. The way he works so hard, I have no doubts about him.
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"For sure, he's going to help the team as much as he can and he understands the pressure now a little bit.
"He should realise how important he will be for the rest of the season."
Zinchenko also suggested Arsenal could deploy a false No.9 system and play without a recognised striker if necessary.
The Ukraine star added: "The most important thing is that everyone is humble and professional.
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"Like you see now, we only have one striker - but we can play with no striker - and everyone needs to play his role.
"Now is the most important of the season and we need to fight for something big."