Bissouma has attracted interest from the likes of Manchester United, Liverpool and Arsenal who played Brighton on the final day of the Premier League season on Sunday.
The Mali international was on the losing end as his side lost 2-0 at Arsenal - with Pepe scoring a brace to clinch victory.
And the Ivory Coast winger continued to produce once the match had finished, according to Arsenal supporters online.
They think he was tapping up the talented midfielder by showing him around their London home.
Footage appears to show Pepe showing Bissouma around the ground as they spoke following the final whistle.
Pepe giving Bissouma a tour of the Emirates, you love to see it pic.twitter.com/JSSAMvRzKx- Blanco:golfer:♂️ (@blanco_x6) May 23, 2021
Needless to say, Pepe's conversation with Bissouma got some Arsenal fans excited on social media.
Pépé showing Bissouma where his family can sit next season.- Val (@ClockEndVal) May 23, 2021
MOTM performance on and off the pitch. pic.twitter.com/yift7aCAqy
Pepe giving Bissouma a stadium tour in preparation for next season pic.twitter.com/djCqhBIqSS- Link Up Arsenal (@LinkUpArsenal) May 23, 2021
Pepe showing Bissouma around the Emirates :red_circle::white_circle: pic.twitter.com/sjKPFnZOgF- jordansana (@jordansana9) May 23, 2021
Pepe giving Bissouma the stadium tour. Tears in my eyes. pic.twitter.com/Nn96uN6fzH- Max ✍ (@AFCMax9) May 23, 2021
Pepe speaking to Bissouma at full time. Think he was telling him 'See you here soon.'- LTArsenal:tm: (@ltarsenal) May 23, 2021
One tweeted: "It's happening isn't it."
A second wrote: "Agent Pepe giving Bissouma the VIP deluxe tour of the Emirates."
A third added: "Pepe and Bissouma not having a discreet conversation in front of the cameras."
Mikel Arteta could probably do with Bissouma in his team following their underwhelming term.
They finished the season in eighth place, one point behind cross-town rivals Tottenham.
Will Bissouma sign for the Gunners? Watch this space.
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