The north London side have been struggling for form in the Premier League in recent weeks and have only won three of their last 10 outings in the top flight.
Arsenal head into their trip to Merseyside in third place in the Premier League table and in the wake of their 2-2 draw with Tottenham at White Hart Lane earlier this month.
The Gunners are 11 points behind leaders Leicester City, although Arsene Wenger’s men do have a game in hand on the Foxes.
However, former Liverpool man Barnes is tipping the north Londoners to drop yet more points when they come up against Roberto Martinez’s men on Saturday.
Writing in his column for Titanbet, Barnes said: “Everton have got the bit between their teeth after the FA Cup win over Chelsea, but this is a must-win match for Arsenal if they still have any hopes of challenging for the title.
“I think they will balance one another out on the day, though. Goalscorers – Romelu Lukaku and Olivier Giroud.”
Arsenal have not won the Premier League since 2004.
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