The decision by Rake, which was announced by airline easyJet Plc (EZJ.L) where he is chairman, helped send shares in Barclays down 3.8 percent at 03.20 a.m. EDT, the biggest losers in the FTSE 100 index .FTSE, having touched their lowest since November.

Rake -- currently deputy chairman of Barclays -- would have had to give up his chairmanships of easyJet and telecoms company BT Group Plc (BT.L) to take the job. Barclays is now expected to look for external candidates to fill the roles of chairman and chief executive, also vacant following the departure of Bob Diamond.

"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," easyJet said, confirming what sources familiar with the matter had told Reuters on Sunday.

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

The next Barclays chairman faces a stiff challenge. The bank was fined $450 million three weeks ago for manipulating Libor, the interbank lending rate which sets an international financial benchmark, and the scandal has unearthed deep problems in its relations with regulators, who have accused it of frequently being too aggressive.

OUTSIDE APPOINTMENT

The job will attract intense scrutiny -- and possibly interference -- from UK authorities, which have been criticized for not doing more earlier to rein the bank in.

Rake's retreat followed protests by several top shareholders who were determined the next chairman should come from outside Barclays, the FT reported on Monday.

Barclays top three executives -- chairman Marcus Agius, Chief Executive Bob Diamond and Chief Operating Officer Jerry del Missier -- have all resigned amid the fallout from the interest rate-rigging scandal.

Agius, chairman for 5-1/2 years, is remaining in his post until a replacement is appointed.

Headhunter Stuart Spencer is helping Agius in the search for a CEO and Ana Mann's MW is helping John Sunderland, a non-executive director at the bank, run the chairman search.

Possible CEO candidates include former Barclays finance director and current advisor Naguib Kheraj; Anthony Jenkins, head of its retail business; and Bill Winters, former co-head of J.P. Morgan's (JPM.N) investment bank.

Candidates for chairman include former top civil servant Gus O'Donnell and Glen Moreno, the former Lloyds Banking Group (LLOY.L) deputy chairman who runs Pearson Plc (PSON.L), the Sunday Times reported.

Anthony Sal, a veteran city lawyer, is expected to be picked this week to lead an investigation into the Libor scandal that the bank has pledged to conduct.

(Additional reporting by Kate Holton; Editing by Neil Maidment and David Holmes)

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