The Gunners are well aware of Atletico’s firm stance that Alvarez is not being allowed to join his preferred destination, Barcelona. Yet the situation is becoming increasingly interesting. Alvarez has recently been jeered by sections of his own support, raising questions over whether he would be prepared to remain in Madrid.
There have been growing whispers over the past 24 hours of Manchester City entering the race to take him back, although that possibility remains uncertain for now.
Sources indicate that, ideally, the Argentina international does not want to leave Spain and the Premier League has not been a major consideration for him this summer.
Arsenal, however, know he is aware of their interest, and sources suggest there could yet be a new willingness to consider a return to England if it means living in London and leading the line for the Premier League champions.
Barcelona, meanwhile, are considering yet another bid - despite the increasingly clear message from Atletico that they will not sell Alvarez to them.
The Gunners’ hope is that, if Alvarez decides he wants to leave, they become the only realistic option he is prepared to seriously consider.
Arsenal believe that once the striker is forced to properly weigh up their proposal, the prospect of moving to north London could quickly grow on him. That is why they have not walked away.
Intriguingly, Arsenal remain in discussions with Atletico over another forward.
Gabriel Jesus has been offered to the Spanish club, and there is genuine interest, potentially creating another avenue through which Arsenal can explore the possibility of an Alvarez deal. There is even a belief that Viktor Gyokeres could enter conversations, although he remains keen to stay and establish himself as a key figure at Arsenal.
Jesus would not be a direct replacement for Alvarez, but the possibility of Arsenal offering an additional forward makes the negotiations particularly intriguing.
At the same time, Arsenal are exploring alternatives to strengthen their left side, with Marseille’s Igor Paixao, Lyon’s Malick Fofana and Everton’s Iliman Ndiaye among those considered. Marcus Rashford and Endrick remain outside possibilities.
Christos Tzolis has already made an impact, but Arsenal’s interest in elite names such as Vinicius Junior, Morgan Rogers, Kenan Yildiz and Bradley Barcola suggests their ambitions extend beyond just adding depth.
Arsenal are still searching for a statement attacking signing - and they are willing to wait for the right door to open.