The 26-year-old has been heavily linked with a move to Catalonia after the 2026 FIFA World Cup following his public statement of wanting a new challenge after two trophyless years in Madrid.
Despite links to other clubs, Barcelona is the only destination he wants, but he remains under contract in the Spanish capital until 2030 - and Barcelona are not in a financial position to meet his enormous release clause.
Los Rojiblancos are still working to convince Alvarez to stay, and they are rumoured to have rejected an offer in the region of €130m from Barca, and Laporta has confirmed talks are ongoing.
"We made an offer to Atletico, we spoke with them, they know the situation. The player wants to come to Barcelona. I have the utmost respect for Cerezo and Gil Marín, with whom I've spoken, and they told me they aren't selling Julian because they have no replacement," as per Diario AS.
"They know our offer and it's firm. We're not at Atletico's mercy, we have a good relationship with them. If they want to consider the offer at some point, we'd be happy to sit down. If they have an alternative, which I hope they do, we can talk. But, our offer isn't open-ended."
Laporta stopped short of confirming when his 'deadline' on Alvarez would expire, but he looks ready to go into the start of the LaLiga season at the end of August without a deal in place, to try and force Atletco to the negotiating table before the transfer window closes on September 1.