Atletico Madrid forward Radamel Falcao, Napoli's Edinson Cavani and Manchester City's Sergio Aguero are the three other targets on Real Madrid's list.
Martinez has hit 30 goals since moving to the Portuguese club from Mexican side Jaguares last summer.
And the 26-year-old is on course to win the Liga Sagres title after Porto saw off the challenge of Benfica in their crunch fixture last weekend.
The report claims Real Madrid are on the look-out for a new striker as they prepare for life without Gonzalo Higuain. The Argentinian international is expected to leave the Bernabeu for Juventus this summer.
Tottenham and Liverpool have also been linked with Martinez, who signed for Porto as a replacement for Atletico Madrid-bound Falcao.
Martinez is one of the most sought-after strikers in Europe following his exploits in Portugal, and Andre Villas-Boas is thought to be ready to raid his old club for the Colombian international at the end of the season.
But with the likes of Manchester United and Real Madrid keeping tabs, the Spurs boss could face a fight to land the forward.
Villas-Boas is eager to bolster his attacking options after struggling through the season with Jermain Defoe hampered by a series of niggling injuries and Emmanuel Adebayor in and out of form.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: http://gms.to/writeforgms