The Ivory Coast international boasts the tag of being Arsenal's most expensive player ever after he arrived in North London for a £72m fee in the summer of 2019.
Pepe has largely failed to live up to expectations at Arsenal, though, and he was only a bit-part player in the side under Mikel Arteta last season.
Bukayo Saka, Gabriel Martinelli and Emile Smith Rowe are all ahead of Pepe in the pecking order, leading to suggestions that Arsenal could try to offload the 27-year-old in the coming weeks.
Pepe only has two years left to run on his deal at the Emirates, but Arsenal are reportedly struggling to find a club who will match their £20m asking price.
Should the former Lille man remain at Arsenal for the 2022-23 season, Mertesacker has backed him to turn his fortunes around and return to his previous goalscoring ways.
"What I've seen in the three weeks when I was coaching there is that he has major potential," Mertesacker told Sky Sports News. "Hopefully we can see that at Arsenal."
Pepe only found the back of the net once in 20 Premier League matches last season - as well as providing two assists - and he only started five top-flight games in total.
Mertesacker was also quizzed on the futures of Reiss Nelson and Ainsley Maitland-Niles, who were shipped out on loan to Feyenoord and Roma in the 2021-22 season.
Nelson was a regular for Feyenoord during their run to the Europa Conference League final, but Maitland-Niles struggled to force his way into Jose Mourinho's Roma XI.
The Arsenal academy manager has admitted that the pair may have to advance their careers elsewhere this summer, adding: "You see them in the leagues of Europe, they went to Holland and Italy, a fantastic experience for them.
"Hopefully they will benefit from that, whether that's here with us or whether they need to go somewhere else, that's obviously a decision for Edu and Mikel."
Mertesacker has overseen two significant changes in Arsenal's academy this month, with Kevin Betsy and Dan Micciche both leaving the club to join the coaching ranks at Crawley Town.
Former Arsenal midfielder Jack Wilshere - who announced his retirement as a player at the age of 30 last week - has now been appointed the Gunners' new Under-18s head coach after completing his coaching badges with the Gunners earlier this year.