The Colombian marksman has netted 41 times in 53 games for Porto - a phenomenal strike rate which suggests he could excel in a more prestigious competition than the Primeira Liga.
Martinez's agent Manuel Manso has courted the attention of big teams, admitting to Tuttomercatoweb that there could soon be a move for his client.
But while Manso insisted that he would waiting until May to make any decisions over Martinez's future, the Italian press are suggesting that the transfer is already in place.
The paper insists that Martinez has personally tried to persuade Porto to lower their demands in order to allow a deal to take place.
It is also reported that Martinez's relatively modest wages at Porto mean that Roma are comfortably able to offer him an improved salary.
Roma are looking to strengthen their striking line ahead of a Champions League campaign next season having emerged as title challengers this season.