The 25-year-old has showed flashes of brilliance since his £72million move from Lille last summer but has ultimately struggled to secure a regular role, and is yet to start a game in the Premier League this season.
Pepe was heavily involved in Arsenal's FA Cup triumph, featuring in both the semi-final and final, but the winger has now fallen down the pecking order once more following the arrival of Willian.
The Ivory Coast international did play 90 minutes as Arsenal reached the Carabao fourth round with a 2-0 victory over Leicester in midweek, playing a key role in the build-up to their opening goal.
And though Pepe has chipped in just eight goals and 10 assists in 45 games, Arteta remains convinced the forward can continue to improve and lock down a role.
"I think he has come a long way, Nico," Arteta said in his press conference prior to their trip to Liverpool on Monday.
"Obviously we know what the club paid for him when he joined and that was obviously an extra pressure.
"He is a really good character to have around and I'm really positive we are going to have him for many years.
"But he is a player who had to adapt, it is a different style and he has a really good attitude and we can see big developments in a lot of places in his game.
"He is very settled here, he is liked by the boys, he is a really good character to have around and I'm really positive we are going to have him for many years and that he can perform at a really high level consistently."