The Colombian forward has been one of European football’s most prolific goalscorers in recent seasons, notching a tally of 72 efforts in 106 outings for the Portuguese giants.
Arsenal have been linked with the 28-year-old on a number of occasions in the past few years, but Liverpool are now understood to be ready to beat their rivals.
Despite signing Rickie Lambert and Mario Balotelli over the summer, manager Brendan Rodgers is worried about his striking options, with Daniel Sturridge having missed much of the last two months through injury.
Balotelli has managed just two goals in that time, while Lambert is yet to find the net – albeit he’s been given very little playing time.
Fabio Borini is also not seen as a suitable player to lead the line at Anfield, which has made Martinez a tempting option for the Northern Irishman.
The South American ace has been at Porto since January 2012, and is thought to be ready to step up to one of Europe’s top leagues.
Liverpool were linked with him when he left Mexican side Chiapas.