The Gunners signed the winger for £72m from Lille, but he has struggled to find his best form since arriving in North London in 2019.
Pepe scored just one goal in his 20 Premier League appearances last season, and although he has two years left to run on his current deal, Arsenal are looking to offload the Ivory Coast international.
According to The Sun, the Gunners are struggling to find a permanent home for Pepe, forcing them to consider a loan departure.
The report indicated that a £25m asking price and Pepe's salary demands are putting off clubs from making an offer.
Pepe is still expected to depart this summer, with a loan move to La Liga a possible option due to an apparent interest from Spain.
The former Lille player has scored 27 goals in 112 appearances for the Gunners.