The Swedish international caught the eye at Euro 2020 and has netted five times during the current La Liga season.
Previous reports have suggested that Isak could be on the Gunners’ wishlist this month, with Mikel Arteta monitoring attacking targets during the January transfer window.
Any deal will come at a hefty price though, with Isak’s release clause reported to stand at around £75million.
Elsewhere, Arsenal have also been linked with a move for winger Ivan Perisic.
The Croatian international is set to become a free agent in the summer with his contract at Inter Milan entering its final months, and Spanish publication Sport suggest that the Emirates Stadium could be a destination for the 32-year-old once his terms expire.
However, they also suggest a deal could be possible this month.
There could also be outgoings from North London, with Sead Kolasinac the latest name linked with an exit - albeit in the summer.
L’Equipe claim that the Bosnian international has entered talks with Monaco over a potential move as he enters the final six months of his contract, with the 28-year-old now able to sign a pre-contract agreement with overseas clubs.
And fellow full-back Cedric Soares has also been attracting interest this month, with the Mail claiming Atletico Madrid are eying a loan move.
Arsenal are reportedly reluctant to let the right-back leave until they secure additions of their own though, with depth in that department a concern at present.