Mikel Arteta's side were interested in the 22-year-old last summer, but the forward shut down hopes of a move to north London when he signed a new five-year contract with his current club last July.
Nevertheless, the Gunners are said to be undeterred and are continuing their hunt for the striker, and have approached Isak ahead of the summer window.
According to Spanish outlet Sport: 'Arsenal have contacted the Swedish scorer's entourage to inform them of his interest and hopes to lower the termination clause'.
It's claimed the Sweden international currently has a £66million [€80m] price tag on his head, slapped on by Real Sociedad last summer in an attempt to deter other interested parties.
However, given Isak's dip in form this season, Arsenal may be able to haggle the sum down to a figure that suits all parties.
Isak earned his new deal after scoring 33 goals across his first two season with the Spanish club, but his form and output has dropped with the youngster landing eight goals in 29 appearances in all competitions, but only four in 20 league games, this season.
The Gunners will be in the market for a new goalscorer come the end of the season following the departure of Pierre-Emerick Aubameyang to Barcelona, and the possibility of an Emirates exit from other striking options Alexandre Lacazette and Eddie Nketiah.
Despite being on the look out for a new addition to the Gunners attack back in January, Arsenal boss Mikel Arteta recently defended the club's inability to bolster their attacking options in the last window.
"When we are in a rush," Arteta stated at the beginning of February, "And the reasons to get a player on board are not the right ones, we didn't do it."
The Gunners aren't alone in their hunt for the Swede, though.
It's understood Barcelona are also keen to secure the former Borussia Dortmund player, having also been interested last summer, should they fail to sign Erling Haaland.
Indeed, it's also been reported that Isak wants to see how negotiations with Barcelona pan out and is focused on the possibility of building his career at the Blaugrana club before going any further with discussions with the north London side.