The Colombian star, who has attracted interest from Napoli, Liverpool and Tottenham, could leave the Portuguese giants if the club's £33 million asking price is met this summer.
Martinez was in red hot form for Porto last season, scoring 26 goals in 30 league games and United boss David Moyes could target the striker as a replacement for Wayne Rooney, who has been subject of two rejected bids from Chelsea.
Moyes has, so far, had a frustrating transfer window after failing in bids for Barcelona star Cesc Fabregas and seeing target Thiago Alcantara opt for Bayern Munich ahead of a move to Old Trafford.
However, with the possibility of Martinez becoming available, United could be set to swoop for the striker in the coming days and he could represent Moyes' first major signing as boss of the Premier League champions.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: http://gms.to/writeforgms