According to a report in the Financial Times today, the BBC boss said that the BBC's commercial arm BBC Worldwide was looking to acquire video-on-demand services and expand its publishing arm overseas.
The corporation is also looking to launch BBC.com as an advertiser-funded website, part of commercial arm BBC Worldwide. The broadcaster already has a large presence online, and only yesterday said that the number of visitors to the website of Radio 1, its national youth music station, had topped 1m.
Thompson said that the challenge to AOL and Google would come from the commercially funded BBC Worldwide and not the publicly funded properties of the BBC in the UK.
BBC Worldwide has offices in North America, Europe, the Middle East and Africa, and the Asia-Pacific region.
The corporation also has a strong global presence through the BBC World Service radio network, which is funded by the UK Foreign Office, and next year launches its Arabic television service.
In other news, Michael Grade, the BBC chairman, is to receive a pay increase of more than 70% when he takes up his post at the soon-to-be formed BBC Trust.
His pay will go up by £60,000 to £140,000, plus expenses, in his new job of chairman of the new body. Grade will chair the new body for four days a week.
Ads for the vacant roles state that the vice-chairman will get £75,000 a year, nearly three times the £28,060 paid to current vice-chairman of the board of governors, Anthony Salz.
Trust representatives from England, Northern Ireland, Scotland and Wales will get £40,000 for two days a week
The Department for Culture, Media and Sport is now looking to fill eight vacant posts at the BBC Trust.
The BBC is currently looking for an increase in the licence fee of inflation plus 2.3% when its current charter period ends in 2007. Many of the BBC's commercial rivals in the UK, including broadcasting rivals ITV, are opposing the increase.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .