Martinez is seen as the perfect successor to Luis Suarez's number nine spot in the side.
Since joining from Liverpool, Suarez has scored 139 goals in five years at Barcelona.
But the Uruguayan turns 33 in January and the club are readying themselves for a new chapter.
Suarez recently publicly acknowledged the fact that Barça were searching for a striker.
He conceded that there would always come a time his body would simply not do what the club expect of him anymore.
The 22-year-old Martinez is at the other end of the playing-career spectrum and Barça are reportedly ready to swoop.
According to Sport, Barcelona's director of football Eric Abidal met with Inter Milan officials this week to discuss the striker's contract.
Martinez is understood to have a €111 million release clause that Barcelona would have to come pretty close to matching.
The report cites a healthy relationship between Barcelona and Inter that may help in negotiations going forward.
Abidal himself recently admitted Martinez was a player the Blaugrana were interested in.
"Yes, he is a complete player, I think he is performing at a great level," he said.
"He is a player we know, there are other players who also have a lot of quality.
"I know Barça, I know what adaptation is like, but I don't pay much attention to the player who plays every weekend, I look at others."
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