They could be officially appointed as soon as today, sources told Sky News.
The group is aiming to bolster its board after a shareholder revolt that kicked off in April when former chief executive Michael Dobson switched roles to become non-executive chairman.
This contravened best corporate governance practice, drawing criticism from around a third of investors.
King is expected to resign from the blue-chip defence giant in the next 18 months.
Duggan was previously an executive at eBay and Skype.
Schroders could not be contacted for comment.