Diario Sport claim Barca will put Griezmann on the market for €100 million (A$186m) in bid to raise funds to trigger Martinez's €111m (A$207m) Inter release clause.
Paris Saint-Germain are speculated to be a likely destination for Griezmann, while it's reported Inter will settle for nothing less than the €111m in a cash lump sum.
Griezmann, 29, became Barcelona's record signing just last off-season from Atletico Madrid in a €120m (A$224m) transfer that angered the Spanish capital club.
The move has not been a roaring success. Although Barcelona sit atop the La Liga table, they have scored fewer goals than in any season in the last decade, with Griezmann in particular struggling for form.
The Spanish media has scrutinised the 2018 FIFA World Cup winner's ability, or lack thereof, to gel with superstar Lionel Messi, with many outlets reporting that the two are not close.
Barca target Martinez, on the other hand, is understood to have an excellent relationship with Argentina teammate Messi.
The Argentina captain has publicly praised the 22-year-old Inter striker, who is enjoying his best season in Europe.
Griezmann has 8 goals in 26 Liga games, two goals in seven UEFA Champions League matches.
Martinez has struck 11 times in 22 Serie A matches, and five times in six in the Champions League.
