Andy Burnham made the offer on Thursday, asking Holyrood to work through Number 10 North and the Scotland Office on arrangements shaped around Scotland's own institutions and geography.
The proposal follows the Government's broader plans to give English mayoral authorities more influence over investment and innovation. Ministers say a Scottish model would be developed jointly rather than imposed from Westminster.
The Government argues that stronger regional partnerships could help connect research, skills, transport and industrial investment beyond the central belt. No new authority, funding settlement or transfer of powers has yet been agreed.
Holyrood retains responsibility for major devolved policy areas, so any lasting settlement would require cooperation between the two governments and support from councils, business and regional bodies.
The offer is a new stage beyond Burnham's earlier announcement of £1 billion in UK Research and Innovation investment and plans for greater local control of existing innovation funds.
The immediate political question is whether the Scottish Government will enter formal discussions and, if it does, how regions would be defined and made accountable.
