The 24-year-old joined the Gunners in a record-breaking £72m deal from Lille last summer and has registered four goals and six assists in England's top flight during the 2019-20 campaign.
However, the Ivory Coast international has often been criticised for a lack of contributions this season, but Arshavin has tipped Pepe to make a name for himself in the Premier League.
Speaking to 888Sport, Arshavin said: "Pepe is a very talented player. He is very quick and a good finisher.
"Already he has done well in part; maybe not as much as he could but I see the potential and he will become one of the biggest stars in the Premier League. He will be huge."
Arshavin netted 31 times in 144 appearances for the Gunners between 2009 and 2013. body check tags ::