Thanks to a tremendous amount of help from @Tsetse_fly I was able to translate and take some meaning from this Linus Omark article by Linus Norberg in Aftonbladet from August 2nd. Norberg spoke with both Omark and his agent Patrik Aronsson and laid out a scenario in with Omark is on the verge of returning to the NHL.
Omark has considered offers from a number of teams and SEL Club Brynäs has pursued him in order to reunite him with past teammate Johan Harju. But Omark is determined to play in the NHL this season, and Aronsson is quoted as saying Omark is close to a deal with an NHL club, but it's not done yet, and he's not willing to name the team.
Omark also told Norberg that the Oilers are "finally" willing to trade his rights.
While there's been speculation that another team (the Coyotes and Panthers have been mentioned most frequently) may send Omark an offer sheet that would require no compensation, the way Omark and Aronsson tell it, Omark is attempting to negotiate his own sign-and-trade deal in order to play in NHL.