Djurgården's latest bid reached £1.5m but was turned down, with Boreham Wood holding out for a fee above that mark plus significant add-ons.
Should the move go through at Boreham Wood's valuation, the 23-year-old would surpass Jamie Vardy's £1m switch from Fleetwood Town to Leicester in 2012 as the biggest fee received by a non-League English club.
In extensive programme notes ahead of Thursday's match against Boston United, Boreham Wood chairman Danny Hunter accused Djurgården of an unauthorised approach for his player and said he felt "backed into a corner" by Abdulmalik downing tools.
"I'm making it crystal clear that we have negotiated in good faith with a club, but we will not relent on the present asking price, as we have already lowered our asking price by £350k," Hunter wrote.
"As far as I'm concerned, the transfer fee is agreed. It's now simply about reaching agreement on some add-ons based on the buying club's league and UEFA success while Abdul is at their club."
Hunter suggested the saga could still end with Abdulmalik staying beyond next Tuesday's deadline.
"If I was a betting man, and I'm not, I would expect, when the transfer window closes, that an unhappy Abdul will still be with us, but what do I know?" he wrote, adding that the player remains under contract for two more years regardless of the outcome.
Abdulmalik, who scored and assisted in last season's National League play-off final defeat by Rochdale, addressed his position directly in an Instagram statement on Tuesday night.
"I'm ready to prove to myself and those around me that I'm capable of reaching the top," he said. "Opportunities like this are rare, especially within the National League where some of the hardest working talent is overlooked. I owe it to myself and the kids growing up just like me to fight for this one I've been offered."
The 23-year-old, released by Millwall's academy in 2024 after representing England at under-17 level, scored 17 goals and added 10 assists last season as Boreham Wood reached the play-off final. Hunter has also accused Djurgården of tapping up the player, a breach that can carry a transfer embargo if proven.