The striker has been strongly linked with the Catalans, but Piero Ausilio says he is unavailable as a release clause was not triggered.
Martinez had been strongly linked with a move to Barca earlier in the year, particularly during the coronavirus-enforced hiatus.
Speculation was rife during that period, with media reports claiming Barca saw Martinez as a long-term replacement for Luis Suarez.
But such has been the in-house turbulence at Barca over the past couple months, especially after Lionel Messi asked to leave, links between the Catalans and Martinez have gone quiet.
Martinez had a release clause in his contract until July but following its expiration, Inter consider the Argentina international to be untransferable.
“There was an approach for the player from Barcelona, but we never started a negotiation,” Ausilio told Sky Sport Italia.
“There was a clause that was never triggered and from the day it expired we considered Lautaro out of the market.”
Ausilio was also quick to stress that Messi would not be moving in the opposite direction.
“You told the truth by saying that there is nothing. I don’t know where certain ideas come from,” Ausilio said of a move for the Barcelona superstar.
“If we talk about Messi, there is no club that doesn’t want to sign him [but] the reality is different. In the market, we must be careful and smart.
“We know what we have to do. First of all, the exits. Through these, we will finance the newcomers. The opportunities are few and the ones we can take are not so expensive.”
But that is not to say Inter will not be doing any business with Barca, as Ausilio also expressed an interest in signing midfielder Arturo Vidal.
“We like Arturo Vidal for sure but he’s a Barcelona player right now,” he said. “If they’ll let him go under the right conditions, we’ll consider signing him.”
Ausilio also added that another midfielder linked with Inter, Chelsea‘s N’Golo Kante, would not be arriving at San Siro.
“We’ve never started anything to sign Kante from Chelsea. No chance. He’s not a target,” Ausilio said.