Bramson’s investment vehicle Sherborne, which owns a 5.4% stake in Barclays, has started talks with the lender about finding a replacement for McFarlane.
The discussions also covered the bank’s use of capital, profits and how costs are structured.
“Addressing these matters could improve Barclays’ financial strength and its long-term competitive position,” Sherborne said.
The activist investor is known for his cut-throat approach to companies he holds stakes in, having ousted the chairman of fund manager F&C and put himself in charge.
McFarlane, who has been chairman since 2015, has previously dismissed reports of an early exit. He told a meeting of shareholders in May that they were “not getting rid of me yet”.
Until now Sherborne has kept its plans for the company private, although he told investors he wanted to scale back the investment bank and improve returns for shareholders.
Despite the calls to shrink the investment bank and focus on retail banking, chief executive Jes Staley has said he has no such plans to bow to the demands.
Barclays plans to meet shareholders, including Sherborne, this month.
Last week Barclays revealed income in the investment bank rose 1% to £5.4bn in the first half, largely due to a strong performance in the equities division.
Total pre-tax profits dropped to £1.7bn in the six months ended June 30 from £2.3bn a year ago after the bank paid £1.4bn in March to settle a lawsuit with the US Department of Justice over the sale of mortgage-backed securities in the lead up to the financial crisis.