Pepe, who arrived at the Emirates Stadium in a big-money move from Lille last summer, scored once and provided two assists as the Gunners beat Newcastle 4-0 on home soil.
Souness was keen to pay tribute to the 24-year-old after the match and even drew comparisons with the club's "best ever player" Thierry Henry.
"I think there is a real, real player in there," Souness told Sky Sports News. "You think of their best ever player Thierry, he came here and didn't have a great first season, took some time, and I see Pepe being a star here, great feet, electric and still a baby."
Pepe has now contributed four goals and four assists in 22 Premier League appearances for Mikel Arteta's side, who have moved into 10th position in the table courtesy of their success against the Magpies.
Next up for Arsenal is a trip to Olympiacos on Thursday night in the last-32 stage of the Europa League.