The Scots-born MP is among the front-runners to replace Theresa May when she stands down.
He insists his plan for Westminster to be allowed to spend Treasury funding in traditionally devolved areas would strengthen the Union.
It could see Westminster funding projects in areas such as education and farming.
The plan would also tackle unrest at Westminster over the Scottish Government’s claim that it alone “speaks for Scotland”.
“There’s a rule that we’re currently bound by, a Treasury rule which means that the UK Government can’t spend money in areas that are devolved,” Mr Gove told a fringe event at the Tory conference yesterday.
“So that means when it comes to promoting culture or supporting agriculture and fisheries, the money has to go through the Scottish Government.
“I think that once we’ve given the Scottish Government their fair share, the UK Government should be able to spend additional money on the basis of need for projects that will strengthen the Union.”
Mr Gove said every government department thinks of itself as a UK department.
Speaking during a question-and-answer session with Stirling MP Stephen Kerr, Mr Gove also hinted UK ministers could start spending in devolved areas.
“The department of education deals primarily with schools in England, but actually the strength of our knowledge base across the United Kingdom matters. “There are English students in Scottish Universities and there are Scottish academics in English Universities - we need to make sure that the money that we spend and the initiatives that we carry out here are badged as UK Government.
“The Scottish Government is very good at using money that it gets form Westminster to claim it is delivering them - actually it is the UK Government that is providing this and leading the way on budgets.”
He hinted that more Scottish MPs would be handed ministerial roles if he replaces Theresa May
“We should make sure the Westminster government is seen as representative of every part of the United Kingdom and we’re prepared to energetically say to the SNP ‘You don’t speak for Scotland.’”
“The whole idea that you say you are the Scottish Government and therefore you are the only legitimate voice that speaks for Scotland is wrong.
“Of course we respect the devolution settlement and we respect their capacity to make policy as long they have a majority.”