The Colombian forward has been heavily linked with the Gunners and the Reds in recent weeks, amid rumours that he will call time on his spell in Portugal at the end of the season.
Martinez has long been considered to be one of Europe’s top strikers, with his tally of 60 goals in 91 outings for Porto one of the most impressive records around.
Arsenal and Liverpool are understood to be considering moves for the £30m-rated ace, but now Spurs are also in the hunt as Mauricio Pochettino plots to bolster his attacking line in January.
The Argentine is believed to be looking to replace misfiring duo Emmanuel Adebayor and Roberto Soldado, and sees Martinez as an option.
Although the Lilywhites cannot offer the 28-year-old Champions League football, ‘Poch’ is hopeful that the lure of guaranteed action at White Hart Lane may sway the South American marksman.
Martinez has been at Porto since 2012, after joining the club from Chiapas in Mexico.