The powers of the Scottish Parliament could be beefed up following a review to be announced by Downing Street.
Powers at the Scottish Parliament could be increased
It is thought the terms of reference will closely follow a motion passed by the Scottish Parliament calling for a review of devolution.
Ministers are also understood to be close to selecting a chairman for the Constitutional Commission.
The body, voted for by MSPs, has the backing of the three unionist parties at Holyrood and Westminster.
Labour, the Conservatives and the Liberal Democrats have been holding discussions for some time.
After the prime minister gave the investigation his blessing last month, Downing Street has begun to become more involved.
Favourite for chairman of the inquiry is either a candidate from Scottish academia or a retired member of the judiciary.
The SNP is not taking part in the inquiry - the Scottish Government is holding its own "national conversation'' on constitutional reform.