The Argentina international has frequently talked up the prospect of signing a new deal with the Serie A champions, as he has now entered the final two years of his existing contract.
However, Martinez is yet to commit his future to Inter amid their financial crisis, and Arsenal are understood to be keeping a close eye on the situation.
A recent report claimed that Martinez would only be open to leaving Inter for either Real Madrid, Barcelona or Atletico Madrid, but according to The Athletic, he could be tempted by a move to the Emirates Stadium.
The report claims that Alexandre Lacazette's name has been brought up during negotiations as the Gunners seek to offload the Frenchman, but Inter are only prepared to accept a straight-cash deal for Martinez.
The 23-year-old - who registered 17 goals and 10 assists from 38 Serie A appearances last term - is thought to be valued at £77m by Inter.