The Boots' chief, who is well-respected throughout the City, has accepted NatWest's offer of a non-executive directorship and formal confirmation of the post is expected shortly.
But Lord Blyth is also to be groomed as a successor to Lord Alexander, NatWest's current chairman, who is expected to stand down next year. The move could see the role of chairman downgraded from a full-time to a part- time position.
Lord Blyth's position at Boots is unlikely to be affected by the NatWest offer. He is to become executive chairman of the retailer later this year in place of Sir Michael Angus, Boots' non-executive chairman, who is retiring.
NatWest is also expected to offer non-executive directorships to one or two other leading City figures in an attempt to inject new blood into its board.
The forthcoming boardroom reshuffle is expected to result in the departure of two non-executive directors - Sir Desmond Pitcher, chairman of United Utilities, and Sir John Banham, chairman of Tarmac.
Institutional shareholders have been pressing for changes to NatWest's board - and in particular the resignation of Lord Alexander - following a series of management crises at the bank over the past year.
Last spring, NatWest admitted that options mis-pricing had left an pounds 80m "black hole" in its accounts, a debacle that resulted in the resignation of Martin Owen, then chief executive of NatWest Markets, the group's investment banking arm.
In the summer, merger talks with both Abbey National, the former building society, and Prudential, the life assurer, collapsed, reportedly causing a rift between Lord Alexander and Derek Wanless, NatWest's chief executive.
In the autumn, NatWest embarked on a costly exit from global investment banking. It sold parts of NatWest Markets for pounds 180m, a surplus of pounds 55m over the book value, but admitted the business had racked up a pounds 210m operating loss during 1997 and the bank would need to take a pounds 270m restructuring charge.
It remains to be seen whether Lord Blyth's appointment will be sufficient to appease disillusioned NatWest shareholders.
A number of institutions have also called for Mr Wanless's resignation and may press for Lord Alexander to depart sooner.
Some in the City believe a merger, possibly with Barclays, is now the only way for NatWest to boost shareholder value.
Martin Taylor, Barclays' chief executive, is known to be enthusiastic about such a match. Mr Taylor approached NatWest last summer to discuss the possibility of a merger, but was rebuffed.
He believes that, in the absence of further rationalisation, the UK banking industry could find itself unable to compete with European "mega- banks", such as UBS and SBC, the merging Swiss banks.
Mr Taylor has reportedly been lobbying senior government figures in an attempt to drum up support for a Barclays-NatWest link-up.