Last December, Thompson unveiled his cost-cutting measures, which involved saving £320m over three years, axing 2,900 staff and moving a further 1,500 north to Manchester.
This month, he will seek approval from the BBC board of governors to add an extra 15% or £50m on to the original £320m figure.
At the FT New Media and Broadcasting Conference last night, Thompson said: "We have done a lot of work since December when the savings plan was announced, and we will put the plans to the governors to sign off at their March meeting."
Areas expected to be trimmed back further include commissioning and professional services, although full details will be unveiled at the end of the month.
The move is likely to anger BBC staff, many of whom have already been affected by the wide-ranging review.
Thousands of staff protested about the job cuts on March 2, the day the government's Green Paper on the future funding of the BBC, which guaranteed the licence fee for another 10 years, was released.
The BBC also unveiled plans for a project called "Creative Futures", which will produce an editorial blueprint for shows, content and services during the next charter period.
The project will separate the BBC into six sectors: journalism; drama; knowledge building; comedy; music; and children and teens.
According to Thompson: "This project is designed to turn the purposes and objectives we set out in Building Public Value and the challenges now laid out in the Green Paper into an inspiring editorial strategy."
Thompson will be sponsoring the project personally with help from BBC creative director Alan Yentob.
The project will be led by BBC deputy director of drama, entertainment and children's division Susan Spindler and BBC controller of strategy Richard Halton.
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