The SPFL held a “positive discussion” on Monday with philanthropist James Anderson over his “extremely generous” offer of financial support.
Chief executive Neil Doncaster and chairman Murdoch MacLennan had talks with the businessman, whose proposal is intended to help all 42 clubs.
Hearts owner Ann Budge told BBC Scotland on Saturday she had spoken to people keen to donate millions.
Doncaster hopes to progress Anderson’s offer “as swiftly as possible”.
He added: “The offer from James is an extremely generous one and we have committed to work together to quickly iron out the details and develop a concrete proposal which could make a significant difference to our 42 clubs.”
Anderson has reportedly said his proposed cash support is not dependent on league reconstruction and “not contingent”.
The Edinburgh-based investor has previously made similar donations to the arts world.
Budge was critical of the SPFL’s initial response after she approached them about the offer of cash backing from business people amid the Covid-19 crisis.
The Hearts owner claimed she was asked to “put a paper in and they will discuss it next week”.
The Tynecastle club themselves have been the recipients of donations, with £8.75m gifted to them since 2017, according to their most recent accounts.
Hearts’ proposal for temporary league reconstruction – which would reverse the Tynecastle outfit’s top-flight relegation – is to be discussed at a meeting of Premiership clubs on Monday.