Sky News has learnt that Babcock has identified Ruth Cairnie, a former Royal Dutch Shell executive, as the preferred candidate to replace Mike Turner.
An announcement about the successor to Mr Turner, one of the leading figures in British industry over the last two decades, could be made as soon as next week.
If her appointment is confirmed, it would make Ms Cairnie the first woman to chair one of Britain’s largest industrial groups – at a time of intense scrutiny of female representation in blue-chip boardrooms.
Alongside BAE Systems and Rolls-Royce, Babcock is a critically important contractor to the Ministry of Defence (MoD).
It employs thousands of skilled engineers in the UK and overseas, providing equipment support, emergency medical services and firefighting capabilities, as well as facilities maintenance through its Cavendish Nuclear division.
Ms Cairnie’s arrival at Babcock would almost certainly lead to her departure from Rolls-Royce’s board, on which she has sat since 2014.
A Brit, she held a series of international roles at Shell including running its global commercial fuels business.
She is also a non-executive director of Primark-owner Associated British Foods and has sat on the board of Keller, the geotechnical contractor to the construction industry.
Babcock began the search for Mr Turner’s successor in January, aided by headhunters at Egon Zehnder International.
The announcement of his departure followed a tumultuous period for the company, which ranks as Britain’s second-largest defence contractor, but also coincided with him having spent a decade as Babcock’s chairman.
UK boards are facing heightened scrutiny of the tenure of their chairs, with revised corporate governance guidelines suggesting they are no longer independent if they have spent a total of more than nine years as a director.
Mr Turner said he would step down at Babcock’s annual meeting in July, having presided over consistent growth in the company’s value and underlying profits since his appointment.
Its shares are, however, about 25% lower than they were this time last year, which is partly the result of souring sentiment towards the wider outsourcing sector and concerns about falling defence spending.
Babcock was also the target of a dossier published by an organisation calling itself Boatman Capital Research, which alleged that the company’s relationship with the MoD – its biggest customer – was “terrible”.
That suggestion was denied by both Babcock, which labelled the claims “false and malicious”, and the MoD.
Mr Turner, who forged a career as one of Britain’s most successful industrialists, has had a difficult 18 months.
As chairman of GKN, the automotive and aerospace group, he led its doomed effort to defend itself from the clutches of Melrose, although he earned some plaudits for the price the company ultimately traded for.
He is also about to step down from the board of Barclays after a brief stint as the bank’s new chairman, Nigel Higgins, reshapes its complement of non-executives.
Babcock has, nevertheless, continued to win sizeable contracts across its quartet of operating businesses.
It recently announced the closure of the company’s Appledore shipyard in Devon, but continues to operate the dockyard and naval base at Devonport, Plymouth.
Babcock, which has a market value of £2.5bn, is highly regarded because of its engineering expertise, particularly in acutely sensitive activities such as its role in maintaining the Vanguard class of nuclear submarines.
Last year, the company took a £120m restructuring charge – or just over £100m after tax – largely relating to its ownership of the Avincis helicopter business it bought in 2014.
However, the majority of the Avincis operations, which are generated from high-margin emergency medical and firefighting activities, have proven to be a compelling growth business for Babcock.
The FTSE-250 company included a statement from a government spokesman in a stock exchange announcement late last year which said it remained “committed to working with [Babcock] on a wide range of programmes”.
The MoD spent more than £1.7bn with the company in its last financial year – a sizeable chunk of Babcock’s overall revenues.
Babcock declined to comment on Saturday, while Ms Cairnie could not be reached for comment.