According to reports in Italy cited by The Daily Express, the Serie A outfit are ready to offer £25 million for the Colombian international as a potential alternative to the likes of Fernando Torres and Edin Dzeko, if indeed they can raise the funds to do so through sales from their own squad.
The same source further suggests that it could be Slovenian goalkeeper Samir Handanovic that is sold in order to generate the necessary cash needed to prise Martinez from the Estadio do Dragao.
27-year-old Martinez is certainly a hot property, with a quite superb record of 18 goals in 26 Primeira Liga games this season.
Such a record has led to much Premier League interest in the player, with London rivals Chelsea and Arsenal - as well as league leaders Liverpool and Tottenham - having been linked with the former Chiapas marksman.
Whether any of those clubs will be willing to match such a potential offer for a player who has yet to prove himself in one of Europe's most reputable leagues, however, is yet to be seen.
While there are evidently a host of clubs chasing Martinez, Chelsea and Arsenal certainly appear to be most in need for a new striker.
With Samuel Eto'o's contract set to expire at the end of the season and doubts surrounding the respective futures of Fernando Torres and Demba Ba, Chelsea boss Jose Mourinho will almost certainly be looking to bring at least one world-class frontman to Stamford Bridge this summer.
Arsenal, meanwhile, are set to lose Nicklas Bendtner when his deal runs out in a few months, something that should surely push Arsene Wenger - provided that he remains in the job for next season, of course - into the transfer market for a new striker with Olivier Giroud's form having declined significantly over recent months.