The newspaper cited a top-10 shareholder who said investors had become disillusioned with BP's choice of successor, Paul Skinner, chairman of Rio Tinto after difficulties at the miner.
Other shareholders still back Skinner, the FT said.
A BP spokesman said no decision had been made yet on a replacement for Sutherland. The Chairman said last year he expected to stand down around the time of the company's AGM in April.
Author: Ksenia Kochneva
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BP Chairman Extends His Tenure
BP chairman Peter Sutherland has agreed to extend his tenure into the autumn amid growing shareholder disquiet over the company's choice of successor, the Financial Times reported on Saturday.