The Sun is reporting that the north London side were keen to bring the 22-year-old to The Emirates during the summer but were unable to push through a deal.
Almiron made his international debut at this summer’s Copa America and had been touted as a possible target for the Gunners this summer.
The same article quotes Almiron’s agent as suggesting that a move to Arsenal in the future could still be on the cards.
Almiron, who is primarily an attacking midfielder, currently plays for Argentinean club Lanus. He joined the Argentinean club last summer following an impressive season with Paraguayan side Cerro Porteno.
He managed to make 17 appearances for Lanus last season. Arsenal have supposedly made a £9.4m bid for the player, but Lanus demanded £11.1m for their player.
The Gunners did not make any signings on transfer deadline day after having wrapped up deals to land striker Lucas Perez and defender Shkodran Mustafi earlier in the week.
Wenger has overseen the busiest transfer window of the club’s history this summer and has spent around £90m on transfers this summer.
The north London side won their last Premier League game as they beat Watford 3-1 at Vicarage Road.
Arsenal return to Premier League action after the international break, when they host Southampton at The Emirates on Saturday 10 September.