The 21-year-old limped off in the first half of the Gunners' 5-0 win over Nottingham Forest at the weekend.
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Saka was on the receiving end of a couple of strong challenges from Forest left-back Renan Lodi.
After receiving medical attention to his ankle, the decision was made from Mikel Arteta to hook him in the 27th minute with Reiss Nelson replacing him.
It led to fears that the youngster could be a doubt for the World Cup with the Three Lions' opener against Iran just three weeks away.
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But according to The Sun, Arsenal are optimistic that Saka will be available for their upcoming London derby against the Blues.
The Gunners will continue to monitor Saka's injury, with the club encouraged by the fact the forward was able to leave the Emirates Stadium without the need for crutches or a protective boot.
Arsenal look set to certainly leave the player out of their matchday squad for their Europa League clash against FC Zurich on Thursday.
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A win for Arsenal against the Swiss outfit will see them finish top of their group.
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But they know that failure to beat FC Zurich may see them finish second if PSV manage to beat Bodo/Glimt.
Should Arsenal end up second in Group A, they could be drawn against the likes of Barcelona, Atletico Madrid, Sevilla or Ajax in the knockout round play-offs.
Speaking after the win over Forest, Arteta delivered a positive update on the fitness of Saka, who has appeared in 17 games in all competitions this season.
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Asked in his post-match press conference whether Saka is a doubt for the World Cup, the Spaniard said: "Hopefully not.
"It was a bad kick right from the beginning he was limping, but I don't see any further than that, let's see how it is in the next couple of days."
Pressed on where he picked up the knock, Arteta remarked: "I think both [leg and ankle].
"He got kicked a few times and he wasn't comfortable to continue."
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