The Argentina frontman has found the net 11 times in 22 Serie A matches this season.
Inter Milan say any club looking to secure Martinez's services will pay €111million - the striker's buyout clause.
Los Cules must pay Lautaro Martinez's release clause if they want him at the Nou Camp.
Inter sporting director Piero Ausilio insists Argentina forward Lautaro Martinez will not be sold to Barcelona or any side except they are willing to pay his release clause.
The Inter star Martinez continues to be heavily linked with a move to the Catalan club, with reports suggesting that the Barca hierarchy see the former Racing forward as a potential replacement for veteran striker Luis Suarez.
Several clubs in Europe have been linked with the 22-year-old, who has found the net 16 times in 31 matches across all competitions.
The Nerazzurri ace has a buyout clause of €111million.
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..."
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