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.”
But that is not to say Inter will not be doing any business with Barca.
The Serie A side have been linked with Arturo Vidal as Barca hold something of a fire sale, and Ausilio says the midfielder is an option for Inter if the price is right.
“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.”
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