Reconstruction has long been on the agenda of both the SFL and the Scottish Premier League, which is currently in charge of the top tier, but the new proposal reportedly favours one overall league body and three leagues of 16, 10 and 18 teams.
These leagues would be made up of existing SPL clubs, the 30 SFL members plus second teams for Celtic and Rangers.
SFL chief executive David Longmuir said: "The SPL are aware of it. It's not something new; these talks have been going on for quite a while.
"The content and the substance of the reconstruction proposal is slightly different, but the actual principle of discussing league reconstruction is not a new subject matter.
"We've been working with our clubs on ideas and how we might wish to take the game forward and how to improve it.
"Tomorrow's the first chance they're going to have to see the detail.
"We're going to be discussing a proposal that might re-energise and refresh the game and be compelling for fans and create a better structure for the game going forward."
The timing is due to "a desire to improve Scottish football," Longmuir insisted.
He added: "It's as simple as that. And to re-engage fans and to give them a compelling league structure which creates a bit of excitement, variety and also engages with investors, broadcasters and sponsors."