The striker's representative claims Arsene Wenger's side, along with Valencia, are considering a move for the Colombia international this summer
The 27-year-old scored 29 goals in 51 appearances for the Portuguese club last season and is in line to feature prominently in attack for Colombia at this summer's World Cup, particularly in the absence of Radamel Falcao.
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.
And the Gunners, along with Valencia, are hot on the tail of Martinez, who has yet to receive any offer from Serie A giants Roma, depsite reports in the Italian press.
"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."
Martinez has previously been linked with a number of other European giants, including Manchester United and Napoli, against whom he scored during last season's Europa League.