The Gunners are at the top of the table after beating Luton Town on Wednesday night.
However, Liverpool returned to the summit on Thursday.
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Asked if they are confident, Zinchenko stated: Yes, I won't lie to you, 100% because it shows that we are ready to fight for it and we are ready to compete with the best teams in the world.
"The result against City was definitely psychologically important.
It's not easy to play against City away and also Liverpool away and the other teams as well - I don't want to be disrespectful to the others. It shows that Arsenal are ready to fight for it."