The British bank reportedly has offered the post to Jes Staley, who is managing partner of US hedge fund BlueMountain Capital Management.
Staley is said to have accepted the role, which has been vacant since Antony Jenkins was ousted in July amid differences over the bank's recovery drive.
Barclays said in a statement that it noted "recent press speculation regarding the potential appointment of Mr James Staley as its new group chief executive officer."
It added: "The process of appointing a new group CEO has not yet concluded and Barclays will provide a further update once that is complete."
The appointment of Staley may surprise analysts given the controversy surrounding the investment banking operation.
Jenkins moved to downsize the division following Barclays's involvement in scandals including Libor inter-bank rate rigging.
One analyst noted similarities between Staley's background and that of Jenkins's American predecessor Bob Diamond, who was at the helm as the scandals broke.
Mike van Dulken at Accendo Markets said: "Note Barclays looking set to name former JPMorgan investment banker Jes Staley as replacement CEO for the ousted Anthony Jenkins. Another investment banker. Another Diamond?"
Other analysts said Staley may have been picked to restore stability and morale in the investment bank, which has been blamed for overall group profitability issues.
AJ Bell investment director Russ Mould said: "Investment banks are generally a good business for employees and a bad one for shareholders, rather like football clubs. Investors tend to attribute a low valuation to them, as they are volatile, cyclical, soak up a lot of regulatory capital and come with high wage bills.
"Any fresh moves to boost returns from Barclays’ underperforming investment banking business will therefore be welcome, especially if its balance sheet continues to shrink.
"A reduced exposure may leave the bank with less potential for growth but it could lower the risks associated with, and improve the predictability of, its overall profits, and therefore prompt a re-evaluation of its shares."
Shares in Barclays fell 7.55p to 249p in mid-morning London trading.