The Ivory Coast international has failed to live up to his £72m price tag since arriving in North London in 2019 and also endured an injury-hit loan spell at Nice last season.
Pepe's contract with the Gunners only runs for another year, and the 28-year-old seemingly has no place in the Arsenal setup under Mikel Arteta, leading to the expectation of a summer exit.
According to transfer expert Fabrizio Romano, Besiktas have a genuine interest in signing Pepe this summer, and the attacker is also pining for a move away from North London.
Romano adds that the Turkish side will soon begin negotiations to discuss the structure of a deal, although it has been claimed that Arsenal could be open to terminating Pepe's contract.
The former Lille man has registered 27 goals and 21 assists in 112 matches for the Gunners since his then club-record move, which has since been broken by Declan Rice's £105m arrival.
Sticking with the theme of Arsenal exits, the Gunners have supposedly agreed a deal to sell Auston Trusty to Premier League new boys Sheffield United.
The American centre-back was signed from Colorado Rapids in January 2022 and excelled on loan at Birmingham City last season, winning their Player of the Year award.
Trusty has featured for Arsenal in pre-season, but he has not played a competitive fixture under Arteta and will likely be allowed to leave for the right price in search of regular game time.
According to the Evening Standard, Trusty is now on the verge of a £5m switch to Sheffield United, who beat out several other clubs to sign the 24-year-old.
Rangers were initially regarded as the favourites for Trusty's signature, while Swansea City and Ipswich Town supposedly had the centre-back on their defensive shortlists too.
Trusty came up with four goals and two assists from 48 games in a Birmingham shirt last season, and he earned his first two caps for the USA national team earlier this year.
Elsewhere in the English capital, West Ham United outcast Nikola Vlasic is reportedly closing in on a permanent exit from the London Stadium after a forgettable two-year spell.
The 25-year-old established a reputation as a goalscoring midfielder during his time with CSKA Moscow and arrived at West Ham for €30m (£25.9m) two years ago, but he came up with just one goal and two assists from 31 games during his debut campaign.
Vlasic was subsequently loaned out to Torino last year and enjoyed better fortunes in Italy, banking five goals and eight assists in 37 matches and starting 29 Serie A games.
Having reignited his career with Torino, Calciomercato claims that Vlasic is now set to rejoin the Italian side permanently, and an agreement is close to being reached with West Ham.
The report claims that Torino are set to meet West Ham's €13m (£11.2m) asking price, as David Moyes's side accept a significant loss on the Croatia international.
Vlasic's camp are supposedly hopeful that a move will be finalised this weekend, as the midfielder follows the likes of Manuel Lanzini and Rice out of the London Stadium exit door.
Finally, Liverpool forward Max Woltman is in talks over a move to Oxford United, the League One side's manager Liam Manning has confirmed.
The Reds academy product has made just two appearances for the Merseyside giants under Jurgen Klopp, featuring against AC Milan and Shrewsbury Town in the FA Cup and Champions League respectively.
Woltman spent the first half of the 2022-23 campaign on loan with League Two side Doncaster Rovers, but he failed to score or assist in 14 games before returning to Liverpool in January.
According to the Liverpool Echo, Woltman has been on trial with Oxford over the summer months, and Manning recently confirmed to reporters that talks over a transfer were ongoing.
However, Manning warned that any move would hinge on agreeing a deal with Liverpool, who tied Woltman down to his first professional contract in January 2021.
Upon the striker's return from his unsuccessful Doncaster loan, Woltman scored two goals in 13 Premier League 2 games for the Reds' Under-21 team.