Their £72million record signing bagged a stunning opener in the 3-0 win over the Molde on Thursday side but the die has already been cast.
He won't feature in today's Premier League fixture against Wolves - or in the subsequent clashes with Tottenham and Burnley - following a red card last weekend.
The Ivory Coast international, 25, was sent-off in the 0-0 draw at Elland Road for headbutting Leeds left-back Ezgjan Alioski.
Mikel Arteta called his actions "unacceptable" but gave the winger a chance to redeem himself on Thursday and is publicly backing his man.
However, behind the scenes the Gunners are ready to offload £140k-a-week Pepe if a suitable buyer can be found.
The former Lille man has been working hard in training but there are growing concerns that he's not cut out for the Premier League.
Since signing for the north Londoners in 2019, Pepe has struggled to hit top gear.
He managed a modest four Premier League goals last term and has scored just once in the top flight this time round.
The fee paid for Pepe 18 months ago remains a bone of contention in The Emirates' corridors of power.
Arsenal bigwigs are now convinced they committed far too much cash - £22m up front and £50m over the next five years - for a player who had enjoyed one solid season in Ligue 1.
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
The deal was put under the microscope again internally this summer as the club overhauled their recruitment team and looked to cut costs.
Arsenal have no intention of letting Pepe leave on the cheap but they would consider a suitable cash-plus player transfer or loan with an obligation to buy.
Arteta will be asked to manage the situation carefully with the club determined to protect the value of their asset.
The Gunners are keen to avoid repeating previous mistakes.
Ozil, who cost £42.5m from Real Madrid in 2013, has been frozen out and is earning £350,000 a week.
No suitors are forthcoming and the German midfielder is content to see out his deal which expires next year.