Qatar Investment Authority, the state sovereign wealth fund which owns Qatar Holding, did not respond to a request for comment.
The share sale comes as Barclays embarks on a shake-up to cut costs and revive its share price, which has halved since Qatar first invested in 2008.
Barclays' stock fell as much as 4.5% in early trading and was last down 2.5% at 1007 GMT.
Qatar became Barclays' largest shareholder during the 2008 financial crisis when it injected 4 billion pounds into the UK bank in a deal that helped avert a taxpayer bailout.
Britain's financial watchdog later fined Barclays $55 million for fees paid to Qatari entities in the 2008 fundraising, which Barclays said it would appeal.
Persons:
Venkatakrishnan, Vekatakrishnan, Iain Withers, Sinead Cruise, Pablo Mayo Cerqueiro, Lawrence White, Danilo Masoni, Andrew Mills, Kirsten Donovan, Emelia
Organizations:
Barclays, Qatar, Reuters, Qatar Investment Authority, Qatar Holding, Thomson
Locations:
Qatar, Germany, London, Milan, Doha