The service would not include programs that are currently shown on US channels such as BBC America, including Doctor Who, Top Gear and the Great British Baking Show, as the show is branded in the US.
An insider said: "We have a huge slate [of programs], and at the moment that slate doesn't all find a home."
The BBC received £226.5 million in returns from commercial activities last year — equivalent to about 7 per cent of its budget, or about half the cost of BBC Two.
It is now targeting returns of £1.2 billion during the next five years — a 15 per cent increase on the previous period. That comes despite falling sales of DVDs, a stalwart of commercial revenues.
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However, the government has promised to consider "the full range of options for reforming the BBC's commercial operations, including full or part privatization".
Lord Hall said that separating the commercial arm would not "make economic sense", at a time when "every major global player is creating a more integrated system".
Increasing foreign sales would boost the TV production sector in the UK, where revenues are growing more slowly than in the US. Deloitte, the accountancy firm, warned in a report that "in general production budgets in the UK are declining in real terms, falling 2.6 per cent on average in the last year".
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That partly reflects constraints on broadcasters' budgets, including the BBC's licence fee.
Last month the writer Armando Iannucci said the BBC should "monetize the bejesus, Mary and Joseph out of our programs abroad" in order to help compensate for the funding squeeze.
The US streaming service — which is yet to be named — would have to overcome several obstacles, including audiences' ability to access the iPlayer illicitly for free when abroad. The BBC is considering requiring users to log in to the iPlayer — a move that would allow a personalized service, but reduce the ease with which UK audiences can access programming content.