It is "clear that there is enough support" for a 14-10-10-10 league set-up to justify an indicative vote of clubs, says SPFL chief executive Neil Doncaster.
Scotland's 42 senior sides have been asked if they would like a permanent change to the divisions.
Plans by Hearts and Rangers failed to attract enough backing, leaving an expanded top flight as the only option.
Doncaster said there is "no reasonable prospect" of a temporary change.
When Hearts were relegated after the Premiership was curtailed, owner Ann Budge proposed the current 12-10-10-10 set-up be changed to three leagues of 14 teams for next season to spare them and other clubs from demotion.
Rangers suggested they and Celtic field 'B' teams in the bottom tier of a 14-14-18 format, but 14-10-10-10 is now the only option after clubs gave their views to the SPFL.
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"It's important to underline that this is not a binding vote and is intended only to steer the board on whether to put forward a formal resolution for voting on, or not," Doncaster added.
"However, the board has judged there is sufficient support for a permanent change to merit this second stage of consultation."
If implemented, Hearts, Partick Thistle and Stranraer would be spared relegation and Kelty Hearts and Brora Rangers - the champions of the Lowland and Highland League respectively - would be admitted to League Two.
Inverness Caledonian Thistle, who finished second in the Championship, would join the top flight and Falkirk would replace them in the second tier with Edinburgh City then moving up to League One.
All 42 clubs have been asked to inform the SPFL by 10:00 BST on Monday if they would support the change.
If there is enough consensus then a formal vote would have to take place at an extraordinary general meeting, and clubs have been asked to allow the notice period for one to take place to be shortened to seven days.
The change would mean allowing two new clubs into the SPFL, which means any resolution would need the backing of 11 of the 12 Premiership clubs, 17 combined from the top two tiers, and 32 from all four divisions.
The league says if the indicative vote shows there is not enough support for the change, then the existing set-up will remain in place.
The Premiership season is due to start on the 1 August with clubs free to return to training from Thursday.