The King wants the law amended so that counsellors of state are working members of the Royal family, the Telegraph understands.
The move would see the Duke of York, the Duke of Sussex and Princess Beatrice all relieved of their duties as official stand-ins for the sovereign, should he be indisposed.
Under the 1937 Regency Act, the spouse of a monarch and the four adults next in line to the throne can be deployed as counsellors of state on official business.
When Queen Elizabeth was still on the throne, those roles were filled by the Prince of Wales, the Duke of Cambridge, the Duke of Sussex and the Duke of York, while the Duke of Edinburgh had also acted as one before his death.
The change in the line of succession means that the new Queen Consort is now entitled to be a counsellor of state, as is Princess Beatrice as the next adult in line.
Buckingham Palace has long been under pressure to eject Prince Harry and Prince Andrew from their roles and install other working members of the family in their places.
It is believed that the King recognises the incongruity of having a trio of non-working Royals able to step into his shoes if he is abroad or incapacitated.
Earl of Wessex and the Princess Royal could take on role
He is thought likely to take the relevant steps to have the law changed as soon as he can, raising the prospect that the Earl of Wessex and the Princess Royal could be elevated to the position.
Such a move may form part of a wider redefinition of working and non-working royals.
As such, if not determined solely by the line of succession as is currently the case, the Princess of Wales may also be included.
It is rare for counsellors of state to be called upon but not unprecedented.
In May, the then Prince Charles and Prince William attended the State Opening of Parliament on behalf of the late Queen, opening the new session after being deployed to deputise for her.