The 23-year-old has been linked with a move to Tottenham amid growing speculation surrounding Harry Kane's future.
However, the Argentina internatonal's representative, Alejandro Camano, quashed those rumours last week and on Monday reiterated that Martinez is eager to reach an agreement.
"We will do everything possible to stay in the Nerazzurri," Camano told FC Inter News. "Martinez is very well in Milan, he has an excellent relationship with his team-mates and with the new coach [Simone Inzaghi].
"He listened to many things, but in no time did he take them seriously: he believes - and we believe - that there is still life at Inter. He believes in the Nerazzurri project.
"He wants to win the Scudetto again with Inter, play a good Champions League with the Nerazzurri and as I said at the moment he doesn't think at all about leaving Italy."
Martinez joined the Serie A champions from Racing Club in July 2018 and has made 132 appearances for the club.
Only Romelu Lukaku's 60 goal involvements rank higher for the Nerazzurri over that period than Martinez, who has contributed 37 goals and assisted 11 in 100 Serie A games.
Martinez also netted 17 goals in 38 top-flight appearances last term, firing Inter to their first Serie A title in 11 years.
He boasted a return of 0.59 goals per 90 minutes last campaign, bettering his 0.51 average in 2019-20 and 0.4 in his first season at San Siro.
Without Lukaku, who joined Chelsea for a reported club-record £97.5 million fee last week, and under new boss Inzaghi, doubts grew as to whether Martinez would stay.
"No, they are private things, between the two of them," Camano responded when asked about Martinez's reaction to Lukaku's departure. "He didn't tell me anything."
Camano says a pay rise is not the priority for Martinez.
"Lautaro is not talking about money, but about football and playing," he continued. "Money is up to your agent.
"At most Martinez can say how happy he is in Milan and the team. I can tell you that I think you need to adapt your situation…. to the new situation."
Inter have also re-invested since Lukaku's departure, bringing in the Netherlands' Euro 2020 star Denzel Dumfries and experienced forward Edin Dzeko from Roma.