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The 26-year-old joined Arsenal from Costa Rican side Saprissa in 2011, and has made 40 first-team appearances for the Gunners in all competitions.
Campbell has not played for the Gunners since the 2015-16 season, however, and spent time on loan at Real Betis last term.
According to Bola VIP, Lazio are considering a move for the attacker this summer, although the Italian side will face competition from Fenerbahce.
Campbell, who will see his Arsenal contract expire at the end of next season, was in action for Costa Rica at the 2018 World Cup.