Martínez started and played 54 minutes as Inter Milan opened their Serie A title defence with a 4-1 win over newly promoted Monza at San Siro, with Marotta addressing the transfer talk directly in comments to DAZN before kick-off.
"Lautaro is our captain and represents the current history of Inter," Marotta said. "I can say there are no circumstances for him to leave Inter. We don't want to give him up for any reason, there's not even any point discussing it."
The Argentina international remains central to Cristian Chivu's plans after finishing last season as Inter's top scorer, contributing to the club's Serie A and Coppa Italia double in the manager's debut campaign in charge.
Marotta also addressed the club's broader transfer strategy with the window entering its final fortnight, striking a more open tone on potential incomings while insisting the current squad is already equipped to compete.
"With Ausilio and Baccin, we are alert to take advantage of any opportunity, also consulting with the coach. Together with the current board, we have made new investments — I can say this squad is competitive as it stands."
New arrivals John Stones and Aleksandar Stanković were among those to begin the season on the bench against Monza, along with Djed Spence and recent signing Curtis Jones, who did not make the matchday squad at all.
Chivu, speaking separately, echoed his president's stance when asked directly about Barcelona's interest.
"I'm not afraid of anything. I'm not here to talk about the transfer market, I'm here to talk about Monza," the Romanian said. "Lautaro is the captain. Probably in these ten days there will be a lot of talk about him, there's always talk about important players."
Pressed further, he added: "Great players always have things around them that coaches don't like, but I believe Lautaro will stay at Inter for a long time. The market is always treacherous, so I can't say what will happen, but we want him to stay."
The reassurances come as Barcelona continue their search for attacking reinforcements with just over a week left in the window, with several avenues already closed off. Julián Álvarez remains unattainable at Atlético Madrid, and Martínez, once viewed as a fallback option, now looks similarly out of reach after both Inter's ownership and coaching staff moved to rule out any departure.
Martínez has scored 174 goals for Inter since joining from Racing Club, making him the club's most prolific foreign player in its history, behind only Giuseppe Meazza and Alessandro Altobelli on the all-time list.