The Scottish Football Association, Scottish Premier League and Scottish Football League have issued a joint statement confirming the discussions, with the matter now set to be taken to the clubs for wider consultation.
The statement read: "All three parties have been involved in productive discussions for some time on the subject of league reconstruction. This culminated in a positive meeting last night (Friday), out of which the two league bodies will now engage in a wider consultation with their member clubs."
It continued: "The discussions are based on the key principles for reconstruction outlined in the Henry McLeish Review of Scottish football.
"Further consultation will take place in the near future, with the aim of reaching a positive outcome on a new model to take Scottish football forward."