The 23-year-old striker has two years left on his Inter contract, but his future at the club has come under the scanner, with Arsenal linked with wanting him.
Inter are believed to be open to selling him to raise funds and he has been attracting the interest of several clubs of Europe this summer.
Atletico Madrid have an interest in him with Diego Simeone believed to be keen to take his compatriot to the Wanda Metropolitano.
But according to Italian outlet Calciomercato.it, the Spanish champions will not be making a move for the forward this summer.
It would take more than €80m to snare him away from Inter and Atletico Madrid do not have the funds to sign the striker in the ongoing window.
Atletico Madrid remain interested in Martinez but they do not have the finances to do a deal this summer.
Arsenal have also been credited with an interest in Martinez with the club in the market for a striker and now have one fewer club to battle for the player following Atletico Madrid cooling their interest.