The SPFL has asked clubs if they would back a 14-team Scottish Premiership for next season and, if not, how might their objections be overcome.
In a letter to clubs in the top two tiers, chief executive Neil Doncaster queried if enlarging the Premiership for five years would be more palatable.
He also asked clubs what other factors should be taken into account around league reconstruction.
Responses have been requested by 17:00 BST on Friday.
Doncaster is also expected to ask similar questions of clubs in Leagues One and Two following their divisional meetings on Wednesday.
The letter comes after talks early this week over Hearts owner Ann Budge's reconstruction proposal.
Budge had suggested a change for two seasons to replace the current 12-10-10-10 configuration - one which would mean Hearts would avoid relegation.
It would also lead to Championship runners-up Inverness Caledonian Thistle being promoted.
It has since been clarified that Budge's focus is on a 14-team top tier, with the lower league clubs agreeing on whatever configuration suits them.
Hearts were condemned to the Scottish Championship in May after the top flight was curtailed.
Before that was confirmed, Budge co-chaired a reconstruction task force which was abandoned when several Premiership clubs intimated that they would not support a 14-team top flight.
Who might be in a 14-team Premiership?