The Scottish Professional Football League's board will meet on Tuesday in the wake of Friday's incomplete ballot.
The league (SPFL) is hopeful of gaining clarity from Dundee over their decisive vote, which could end the lower league season.
The fate of the campaign rests on the Championship club, who asked for their initial no vote not to be considered, according to the SPFL.
Reports on Tuesday claim Dundee are now close to voting for the proposal.
If passed, the Championship, League One and League two would finish now on a points-per-game basis. The Premiership season would also be ended if the SPFL board "determines the games cannot be played".
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Friday's ballot led to chaotic scenes in the days that followed, with top-flight club Rangers calling for the suspension of SPFL chief executive Neil Doncaster and legal adviser Rod McKenzie, as well as an independent investigation into the ballot.
Hearts owner chairman Ann Budge has also accused the league of trying to "unduly influence" the vote and vowing to propose league reconstruction.
For the SPFL motion to be passed, it needs nine Premiership clubs, eight in the Championship, and 15 in Leagues One and Two combined to vote in favour.
The threshold has already been reached for the Premiership and the bottom two leagues, with the Championship just one vote short.