Sir Roger is thought to be in advanced discussions about the high-profile role at the FTSE 100 group.
He is due to step down from his post at the CBI in June, at the end of a two-year term at the top.
BAE Systems’ current chairman Dick Olver is due to step down in May 2014.
The firm has tasked senior independent director Nick Rose and headhunter Spencer Stuart with sounding out possible replacements for Olver. Rose has been seeking out candidates since January.
Others who have been linked to the role include former Rolls-Royce boss Sir John Rose.
A decision is expected in the next month or two.
The new chairman would need to be approved by the government, which holds a so-called golden share in formerly state-owned BAE and can veto certain actions.
Olver, a former BP executive, has been in the chairman’s seat for nine years. He is contracted to work at least two days a week for a £725,000 salary.
He has helped steer the firm through a tough round of state spending cuts in recent years, as recession-hit governments around the world pledged to rein in costly defence programmes.
Olver was the subject of a shareholder revolt late last year led by fund manager Neil Woodford, who runs money for Invesco Perpetual, over the failed attempt to merge BAE System with fellow aerospace giant EADS.
The tie-up collapsed last October as the UK, French and German governments voiced concerns about the international defence deal.
A spokesperson for BAE Systems declined to comment on the recruitment process yesterday.
PROFILE: SIR ROGER CARR
SIR ROGER Carr, 66, has spent much his career steering British institutions. As well as his current roles at the CBI and Centrica, he was in the chair when confectionary group Cadbury was controversially sold to US rival Kraft.
He stepped down from the Bournville-based company following the takeover in 2010, but stood by his role in turning around a company that was once “unloved and unwanted by the UK investment community”.
Sir Roger is an independent director at the Bank of England (a role that ends in May 2014, around the time the BAE chair becomes vacant) and a senior adviser at KKR. He has previously served on the boards of Thames Water and Mitchells & Butlers.
He puts his expertise to good use as a visiting fellow at Oxford’s Said Business School, and was among the judges at last year’s City A.M. Awards.
He was knighted in 2011 for services to business.
Given his British business pedigree, BAE is believed to be willing to overlook Sir Roger’s lack of defence experience.
He is in any case well-connected enough to take tips from those at the very top of the industry. Sir Roger will soon get the chance to talk with his potential predecessor about the benefits and pitfalls of the BAE chair – both he and Dick Olver are members of the Prime Minister’s business advisory group, which is due to hold its quarterly meeting today.