Scotland is the most devolved part of the UK, with powers over health, education and transport, as well as the ability to administer benefits and set taxes.
However, the Scottish government has not adopted the English system of regional mayors, who have considerable powers in their areas.
Burnham called for power in Scotland to be decentralised.
He suggested that employment support, for example, could be reformed to give more control to local grassroots organisations.
This could allow for different employment support systems to be set up in different parts of Scotland, depending on the needs of each area.
