According to Jose Gonzalez of Sport, the Slovenia stopper is currently Arsenal's "main objective" for the end of the season, as manager Arsene Wenger is keen to strengthen his options between the sticks. Paris Saint-Germain are also noted as suitors for the Atletico star.
In addition, James Olley of the Evening Standard has also suggested the Gunners have been keeping an eye on Oblak.
"The quality of player Arsenal can attract, however, will be influenced by whether they can offer Champions League football," Olley added. "A second year without that income stream would also reduce the money available to spend on players."
Per Gonzalez, it's suggested Arsenal want a new goalkeeper to replace Petr Cech, who is now 35.
The former Chelsea man has been a long way below his usual best this season.
Journalist Jonny Sharples commented on his disappointing form after the goalkeeper made a comical error in the recent 3-1 loss to Swansea City:
While Cech was hailed as a wonderful signing for the Gunners, issues at the back have remained for this side. Much of that is down to poor protection in central midfield and in the heart of the team's defence, but Arsenal may feel as though they can find an upgrade on their current starter between the sticks.
Oblak would be one, as the 25-year-old has developed into one of the best goalkeepers in the world during his time at Atletico Madrid.
Since arriving in the Spanish capital in 2014 from Benfica, he's made remarkable progress and is now a crucial part of the meanest defence in La Liga. Incredibly, Atletico have conceded just nine goals in their 21 top-flight matches this season.
As noted by OptaJose, that's a trend that runs back to the early stages of Oblak's Atletico career:
Looking at the Slovenian's game, it's tough to find too many weaknesses, and he gives the side so much assurance in their defensive play.
Oblak is dominant under the high ball and quick off his line when it comes to one-on-one situations. Additionally, he's a stunning shot stopper, and although Atletico are tremendously organised, the 'keeper often delivers when he is called upon.
As relayed by This is Anfield's Jack Lusby, Oblak is the latest in a long line of exceptional goalkeepers to line up for the Madrid side:
If Arsenal or PSG were able to get him, then it'd be a massive boost. Oblak is not only among the best in the world in his position as things stand, at 25 years old, he still has experience to accrue and progress to make.
At the moment, it's tough to envisage a scenario in which he ends up at Arsenal, though, especially with the Gunners off the pace in their pursuit of UEFA Champions League qualification. If Atletico are willing to sell Oblak in the summer, you sense some of Europe's biggest names will be in the hunt.