The powerful forward has emerged as one of European football’s top marksmen since joining the Portuguese giants from Chiapas in Mexico during 2012.
Chelsea, Liverpool and Manchester United have all been linked with moves for his signature, but Arsenal could ensure that they get their man with a £35m offer.
Porto are currently trying to tie Martinez down to a new deal to raise the fee needed to break him free of his contract, but the 27-year-old is said to be stalling.
After calling off a possible move for Mario Balotelli, Wenger is still thought to be looking for a striker and has revived his serious interest in Martinez after his double World Cup strike against Japan.
The Frenchman was frustrated at reliance in Olivier Giroud last season, and is keen to bolster his options in a bid to mount a sustained title charge.
QPR’s Loic Remy is also an £8m target.