The current Barclays plan is to install a senior figure at a newly created level in the hierarchy immediately below Andrew Buxton, who would remain as chairman.
The difficulty of making the split without antagonising Sir Peter and other essential members of the top team has become the main obstacle slowing the reorganisation demanded by institutional shareholders.
Sir Peter has had a key role in developing group strategy, as well as chairing BZW. So if Mr Buxton's role is to be a full-time chairman and a chief executive is appointed beneath him, it could have a significant impact, since a chairman is expected to concentrate on the big strategic issues.
There are fears that Sir Peter would not be the only top man to quit if the new structure interposes too powerful a chief executive between Mr Buxton and the existing team.
Sir Peter is known to have had a series of potentially lucrative approaches from other companies, said to have been prompted by news reports about the crisis at the top of Barclays.