In-form 22-year-old Martinez has a release clause of €111 million, which Barcelona are strongly considering meeting, according to Calciomercato.com.
Coach Antonio Conte is reportedly looking to the Premier League as Inter prepare for the possibility of losing their number 10 - namely at Manchester United's Anthony Martial and Arsenal's Pierre-Emerick Aubameyang.
Aubameyang's contract with Arsenal expires in 2021, and the Gabon international is said to be restless in London.
He could be open to a return to Milan, especially if Arsenal miss out on UEFA Champions League football.
Another option the Nerazzurri have been keen on in the past is Martial.
It is claimed he's back on Inter's wishlist after a strong second half of the season, and the club would be keen to partner him up front again with former Red Devils teammate Romelu Lukaku.
Aubameyang has 17 goals in 26 Premier League matches this season, while Martial has bagged 11 in 23.
