Lord Patten said the BBC could also lose one of its main sporting events, as without the "financial firepower," bidding for any sports rights would be "extremely difficult" and losing some sports rights looks likely.
Lord Patten said the channel was "bound to face some tough decisions in the area of sport".
With the BBC aiming to find 20% savings over the next five years after last year's licence-fee settlement, Lord Patten said the digital channels Three and Four were also under review.
However, he has vowed to fight to save the World Service from the spending cuts and will urge foreign secretary William Hague to protect the service, which he described as "the core of what the BBC is doing."
This article was first published on brandrepublic.com