The Gunners are believed to be lining up forward-thinking reinforcements after losing Theo Walcott for the remainder of the season through a knee injury.
The England international’s absence will put a real strain on the club’s centre-forward options, with Olivier Giroud now their only orthodox player in the role, with Nicklas Bendtner also on the sidelines with fitness concerns.
Martinez has been on the Londoners’ radar for some time, with the Colombian having emerged as one of European football’s top talents since joining the Portuguese champions from Mexican side Chiapas in 2012.
A loan deal for Real Madrid’s Alvaro Morata is Arsene Wenger’s preferred option, but in case the Spaniard won’t be available Arsenal are lining up the South American hitman.
Martinez won’t come cheap, with his club side rumoured to be holding out for a release clause-triggering offer of £33.2m.
The powerful striker has netted 14 goals in 20 appearances this season, two of which have come in the Champions League.