The striker's representative claims Arsene Wenger's side, along with Valencia, are considering a move for the Colombia international, who scored 29 goals last season
The 27-year-old scored 29 goals in 51 appearances for the Portuguese club last season and is in line to feature in attack for Colombia at this summer's World Cup.
Arsenal, who are currently in talks to re-sign Carlos Vela from Real Sociedad, are in the market for another forward this summer in order to provide competition for Olivier Giroud.
"In Italy we have had very little contact, but for sure there have not been any offers from Roma," Peppino Tirri, Martinez’s agent in Italy, told Calciomercato.
"There are, instead, opportunities abroad - Arsenal and Valencia in particular are very interested in Jackson Martinez."