Atletico Madrid chief executive Miguel Angel Gil Marin gave the clearest indication yet of the club's position on Friday, insisting there is no offer big enough to change their minds.
"My opinion is clear, the club's will is clear, we've made it known to the player, to the agent, to Barca's president," he said.
"We don't want to transfer him, we don't accept the offer of 100 million euros and we won't accept one of 150 or one of 200."
Alvarez himself has previously said a transfer would be the best outcome for all parties involved, repeating as much again in recent days, though his message was notably less forceful the second time around.
Barcelona are said to have concluded that, unless the Argentina international forces the issue with Atletico's hierarchy himself, there is no realistic route to signing him.
According to reports in Spain, Barcelona will give themselves until July 31 to establish whether a deal is possible before moving on. Club president Joan Laporta hinted at the deadline last week, saying the club's offer "is not infinite" and admitting it could be withdrawn shortly.
If no breakthrough materialises by then, sporting director Deco and head coach Hansi Flick are expected to turn to alternative targets for a new centre-forward.
Reports in the Spanish press have suggested funds could be freed up for the market following a €105m bond issuance the club completed this week, although Barcelona have stated that financing is earmarked for the ongoing Espai Barca stadium redevelopment rather than player transfers.
Should the move for Alvarez fall through, Barcelona could turn to players already in the squad to fill in as a false nine, with both Dani Olmo and Ferran Torres having experience in the role for club and country.
There is also growing talk of Lamine Yamal eventually shifting into a more central position over time, similar to the evolution Lionel Messi underwent during his own career, though signing an out-and-out striker remains the priority for now.