Barcelona see Martinez as their ideal long-term striker signing and ultimate successor to Luis Suarez.
Suarez's serious injury earlier in the season accelerated the Catalan club's efforts to hunt for a younger alternative.
The Uruguayan is now 33 years old and has been informed that the club are searching for replacements according to Barcelona's director of football Eric Abidal.
"I am transparent with the players, Luis can tell you because last year I already told him that it was going to be like that," he said.
"That we were going to look for an offensive player and I don't say he did not accept it, he accepted it because he wants the best for the team."
Martinez is reported to have a £92m release clause in his contract which Barcelona are expected to activate in the summer.
Inter's ultimate preference would be the midfielder Arthur Melo, who is an integral part of the current Barcelona side.
The Brazilian is understood to be viewed as key to La Blaugrana's future plans, so it seems unlikely Inter will see their wish granted.
Inter are also said to be interested in two of Barcelona's fringe players currently out on loan.
The Italian outfit are also said to be exploring moves for Atalanta's Duvan Zapata and Chelsea's Olivier Giroud as replacements for Martinez.
