Mikel Arteta is keen to bolster his midfield this summer and sees Partey as the ideal target, and there were hopes that Arsenal would be able to negotiate a cut-price fee as a result of the 27-year-old's hesitance to sign a new contract.
Arsenal have already seen one bid knocked back, and as noted by The Guardian, a second offer has failed as well. This time, the Gunners offered €25m (£23m) plus French midfielder Mattéo Guendouzi, but Atléti were not interested.
Los Rojiblancos have made it clear that Partey will not leave unless any interested side pays his £45m release clause, but Arsenal have previously warned Atléti they have no plans to cough up that kind of money.
Not only does this now leave Arsenal pondering what to do about Partey, it also presents the question of what to do with Guendouzi, who was banished from training after a clash with Brighton's Neal Maupay triggered a fall-out with Arteta.
A swap deal involving Barcelona has been suggested, with either Philippe Coutinho or the pairing of Arturo Vidal and Ivan Rakitić touted as potential targets.
Get French Football News state there are yet to be any formal negotiations with Barcelona, but Guendouzi is hoping there soon will be as his preference would be to join the La Liga giants in the near future. The player's agent remains in contact with officials at Camp Nou.
A deal with Barcelona may yet be a possibility. Sport believe Coutinho has left the door open to a move to Arsenal and has asked for more time to weigh up all his options this summer.
Coutinho's agents are currently scouring Europe for interested sides and are expected to make a decision on his future next week. Given the instability of the current transfer market, he may not have many suitors to choose between.
Arsenal's preference is still to use Guendouzi as a makeweight in a deal for Partey, but with that looking unlikely, swapping him for Coutinho may be the next best option.