Reports stated earlier this week that Atletico Madrid had given Alvarez until Sunday to decide whether he will stay or leave this side this summer, with the window set to close in less than a week.
Atleti fans have booed Alvarez after learning of his desire to join Barca, and they have made it clear that he has no future with the side.
Despite his desire to leave, transfer expert David Ornstein reported this weekend that Alvarez does not have any ambitions to join Arsenal who are now the only club in the running for him.
The striker has reportedly spoken to manager Mikel Arteta, rejecting a switch to North London in what is a crushing blow for the Gunners.
"At the time of reporting, it's a low chance that he will come to Arsenal, because he's had his heart set on Barcelona," Ornstein said via TNT Sports.
"Atletico have closed the door to Barcelona, that won't happen. They would do a deal with Arsenal, Arsenal are prepared to reach an agreement club to club. But they would want the player to want to join them and he's shown no indication of wanting to at this point.
"He's spoken to Mikel Arteta and said he doesn't want to come. That could change - could he soften in the days ahead? These situations are always moveable feasts, so I don't want to pin my colours to the mast and say it won't happen, but right now it's not developing in the way that some have suggested.
"I think that would be the target for Arsenal - Julian Alvarez - and if they don't get him maybe they go with what they've got. But we don't know until the deadline."
Alvarez has four years left on his contract with the Spanish giants and after finding the back of the net 49 times in 107 games across competitions, it’s looking increasingly likely that he will stay in a piece of news that will only infuriate Atletico fans.