The Brazilian winger, 25, has impressed in Portugal this season, scoring six goals and providing five assists in all competitions to help Porto win the league title.
Pepe joined the two-time European Cup winners ahead of the current season after helping Gremio win four consecutive Brazilian titles. He is yet to win a senior cap at international level.
If the Gunners complete a deal for Pepe, he will be the second Pepe in their squad after Nicolas Pepe.
The talent's existing deal doesn't expire until June 2026, yet Arsenal can release him from that by triggering his reported €60m clause (around £51.3m). The Gunners may tempt the Portuguese giants with a lower offer for Pepe if rumours are to be believed.