The Argentina international is Barca's top target for the summer market on recommendation of club captain Leo Messi.
Messi is a big fan of his Argentina teammate and has urged Barca's board to bring the striker to Spain this summer.
FCInterNews reports a first bid has been lodged, though it falls short of Martinez's €111m buyout clause.
Instead, Barca have offered €70m cash plus Nelson Semedo and Arturo Vidal. It's suggested Semedo is rated at €30m by Barca and Vidal €20m - valuations Inter dispute.
For the moment, Inter haven't responded to Barca's proposal.