The 12 Scottish Premier League clubs met last week to discuss a number of options for introducing play-offs between the top two divisions.
Since then, 10 clubs sent a proposal to the SPL asking to join their ranks in a breakaway from the Scottish Football League.
Dundee, who were relegated on Sunday, have a foot in both camps as they will be able to speak for their future second-tier colleagues. It is understood there are three options other than the status quo that will be discussed by the 12 clubs.
One is the introduction of play-offs between the SPL and SFL. The second is the introduction of play-offs in a new structure with an all-through distribution model with the other option being the possibility of an SPL2.
St Mirren and Ross County both vetoed plans for a new merged structure last month after being unconvinced of the merits of the proposed split of the top two divisions into three after 22 games.
Both clubs are understood to be more favourable towards play-offs and have publicly questioned the wisdom of a split, but other clubs might need to be convinced over opening themselves up to an increased chance of relegation without creating enough extra revenue for the second tier.
There are just five weeks left until the fixtures are due out, with the SPL season scheduled to start on August 3, but it is understood league officials are comfortable that any agreement could be actioned at any stage before the publication.
Dundee manager John Brown is optimistic some progress can be made.
Brown told BBC Scotland: "I think tomorrow could be the point where we get a decision. What I'm hearing, there will be decisions made tomorrow and hopefully it's for the best of Scottish football. We need to do it soon. We're becoming a mockery here - we need to come up with the answers."