BVB see the Colombia striker, 26, as a potential replacement for Robert Lewandowski next season, while Rafael Benitez's side are still looking to fill the void left by Edinson Cavani's departure to Paris Saint-Germain.
Porto have already lost influential figures in Joao Moutinho and Jamez Rodriguez to Monaco this summer but Martinez insists he is not about to follow in their footsteps and exit the club.
"I am happy to be here at a club like this," he told Renascenca.
"I am enjoying the opportunity to play here.
"I want to repeat what happened last season and win more trophies with Porto."
Martinez, whose contract runs out in 2016, scored 26 goals in 30 league games last season.