Two months after announcing it was open to offers, Valiant Petroleum told investors the senior non-executive director Michael Bonte-Friedheim has been appointed acting chief executive.
The company said it has agreed with Mr Buchanan that he should "focus exclusively" on the delivery of a proposal to buy the business he founded in 2004.
Mr Buchanan owns 7.7% of the shares in the company. The stake is valued at around £14 million based on the company's market capitalisation of £180m.
The company said work on the strategic review it announced in September is ongoing.
The company added: "Peter will remain a director of Valiant but will not participate further in discussions related to the process. Mike will lead the evaluation of all of the alternatives being considered."
In September, Valiant posted an interim loss of $44m (£28m). With assets in the North Sea, Norway and the Faroe Islands, Valiant suffered exploration reverses in the first half.
On Monday the company said it had started production from the Causeway oil field in the Northern North Sea.
The shares closed down 8.25p at 441.75p.