Rake, who is also chairman of low-cost airline easyJet, did not say whether he would leave Barclays.

"EasyJet confirms that Sir Mike Rake has informed the easyJet board that he has formally informed the chairman of Barclays that he does not wish to be a candidate for the chairmanship of Barclays," the airline said in a statement.

"The board takes the opportunity to repeat its support for Sir Mike."

Barclays wants a new chairman to replace outgoing Marcus Agius, who earlier this month announced his intention to resign from the bank over an interest rate rigging scandal that has badly damaged the lender's reputation.

Barclays' former chief executive Bob Diamond and its chief operating officer Jerry del Missier also stepped down over the affair.

Barclays was recently fined £290 million ($451 million, 371 million euros) after admitting that it attempted to manipulate the Libor and Euribor rates between 2005 and 2009.

Libor (London Interbank Offered Rate) is a flagship London instrument used as an interest benchmark throughout the world, while Euribor is the eurozone equivalent.

The rates play a key role in global markets, affecting what banks, businesses and individuals pay to borrow money.