To be announced today at the party’s Dundee conference the scheme, if ever adopted, would see a national board set maximum rent prices based on factors such as heating and insulation quality.
It would aim to create what’s perceived to be a fairer system by preventing landlords from inflating prices simply because of location.
As part of a wider scheme there would also be a new council house building programme bolstered by investment from council pension funds.
A main aim would be to tackle “rip-off rents and agency fees” to create better living conditions for families.
In some areas of the Central Belt, for example North Lanarkshire, private rents can be a substitute for social housing because of the volume of demand - and some rents are claimed to be unreasonable.
Mr Leonard will tell the conference that “The Mary Barbour law” will regulate private rents to ensure no one has to rent a sub-standard home, or one that pushes them into poverty.