The Prime Minister will say at an event in Lanarkshire on Friday that the Scottish Government is one of the most centralised devolved administrations in Europe.
The Prime Minister will say at an event in Lanarkshire on Friday that the Scottish Government is one of the most centralised devolved administrations in Europe and that Holyrood is not giving people who know their areas best enough of a say, despite significant devolution from Westminster over the last 27 years.
The Labour leader will also say that the next stage of devolution should place more decision-making in the hands of Scotland's regions and cities to drive reindustrialisation.
Mr Burnham will urge the Scottish Government to work with No10 North and the Scotland Office to push more power into Scottish regions.
He said: "During my first week in office, I told the First Minister that I wanted to work with him to spread opportunities to communities across Scotland's regions and cities.
"Through No10 North, we are rewiring the state and I want to make sure regions in Scotland are fully part of this.
"This is me making an offer to the Scottish Government. With us working together, there is no limit to what we can achieve for the Scottish people."
Scottish Secretary Douglas Alexander said: “Devolution has done a great deal, but power was never supposed to stop at the doors of the Scottish Parliament. People in North Lanarkshire, in Fife or in the Highlands know what their communities need better than any minister, whether they sit in London or Edinburgh.
"The Prime Minister's offer to the Scottish Government is a genuine one, and the Scotland Office is ready to roll up its sleeves alongside them to make it happen. Two governments, one goal - good jobs and real opportunity in every corner of Scotland.”
Read more: Andy Burnham 'can't pick and choose when democracy applies', says Nicola Sturgeon
Mr Burnham’s visit to Scotland comes during the SNP’s annual conference in Aberdeen. The Nationalists have since invited him to attend their conference while he is north of the border.
This is set to be his first big event in Scotland since becoming PM in the summer. He visiting Glasgow during the Commonwealth Games but has not held a press conference.
Mr Burnham took a swipe at Mr Swinney during his own conference speech in September, after the SNP leader claimed he would be the last UK Prime Minister.
The Labour leader revealed that the comments came on the day that his dad died and that they made him “utterly determined to prove him wrong”.
He then made a blistering defence of the union, detailing the “good life” the UK had given his father.
He said that the UK he “believes in” is “A union of nations that gave trade unions and the cooperative movement to the world, the National Health Service. A country that stood up to fascism a country of solidarity, not separation.”
Read more: Andy Burnham 'determined to prove John Swinney wrong' in blistering defence of union
Mr Burnham caused a frenzy amongst pro-independence politicians in the House of Commons a few weeks ago by saying Scotland was in the exact same situation as Northern Ireland when it came to independence.
Northern Ireland has a constitutional arrangement that allows it to leave the UK, while Scotland does not.
Mr Swinney made his comments at an independence summit in Cardiff with the nationalist leaders of Wales, Northern Ireland and Sinn Fein’s Republic of Ireland leader.
Mr Burnham - the former mayor of Greater Manchester - has vowed to extend devolution in England.
He has said that political power has been centralised and will give more powers to English regions.
Deputy First Minister Jenny Gilruth said: “It is very welcome that the Prime Minister is coming to Scotland to participate in the Scottish Government’s consultation on the opportunities posed by public service reform.
“The First Minister has been on record for many months saying that he wishes to work with Mr Burnham on this issue, and the further devolution of powers to the Scottish Parliament, and told him that personally when they met the last time he visited Scotland in July.
“Our focus is on delivering stronger and efficient citizen-centred public services that are sustainable for generations to come, and our work on delivering the changes necessary to support the needs of diverse communities across Scotland has been taking place for over a month.”