Argentina striker Martinez has long been linked with a move to Camp Nou as a potential long-term replacement for Luis Suarez, but striking a deal appears to be complex.
Barca was struggling to free up significant transfer funds before the coronavirus crisis and are said to be prepared to sell a host of squad players and offer others in part-exchange deals in a bid to land their top targets.
Arturo Vidal, Nelson Semedo, Samuel Umtiti and Ivan Rakitic have all been touted as possible makeweights in any deal for the former Racing forward.
Inter, though, have made it clear that any club interested in Martinez will have to pay the full amount of his reported €111million buyout clause, which is said to contain certain clauses including the fact that it must be paid in a single instalment.
Ausilio told Sky Sport: "Lautaro Martinez is not for sale. Barcelona contacted us, we have a good relationship, but we told them we'll not sell Lautaro.
"If they want him, Barca must pay the full release clause.
"We want Lautaro in our team in the future. He will not be sold; the release clause is the only way. Barca know this as do the other clubs who contacted us. And Lautaro's release clause is so complicated..."
Chelsea and Manchester United have also been linked with the 22-year-old, who has scored 11 goals in 22 Serie A appearances this season as part of a formidable Inter attack alongside Romelu Lukaku.