Drakeford said the “basic responsibility for a Welsh government is to speak up for the things that matter here in Wales and it really doesn’t matter who is in power in Westminster”.
He told BBC Wales that the other UK nations that are subject to the formula would need to be persuaded.
He said it was a two stage process:
“There are things that need to be done to the Barnett formula itself… to make that formula work better and to be fairer.
“We’re having productive discussions, not only with the UK government, but with Scotland and Northern Ireland as well as to how we can make the present system work better for us all.”
Beyond that the Welsh government has an ambition “for a new formula”, the finance secretary said.
“You have to assemble a lot of political support for that, not just from the UK government, but Scotland, which does very well out of the Barnett formula, and Northern Ireland, who’ve done very well out of it in more recent times.
“We’re not going to do that in the short run, I believe. But that doesn’t mean we stop making the case.”