The deal will give Channel 4 the rights to broadcast the interview in the UK and to sell it worldwide other than in America and Canada. It is likely to be conducted by the newscaster Jon Snow, and would include an assurance that she will be frank about details of the affair.
Last night, the agreement had still not been signed, leaving room for competitors to make a bid. A Granada spokesman said that it was "still in serious negotiations". However, the amount of money has been agreed with Channel 4 and details on the lines of questioning were being ironed out.
Miss Lewinsky is said to want to tell her story before America's house judiciary committee releases tapes of her conversations with Linda Tripp about "the big creep", which could occur within two weeks. Her lawyers fear that once the world has heard her voice on the Tripp tapes, the mystery element of her testimony will be devalued.
The American rights to Miss Lewinsky's story have been the subject of much wrangling. The talk show host Oprah Winfrey offered $1m, but negotiations fell apart when Miss Lewinsky's lawyers tried to retain the world syndication rights. The comedian Roseanne Barr then stepped in, also offering $1m, but that deal also crumbled.
The front-runner is now the ABC network, with the interview to be conducted by Barbara Walters.
The pay-out to Ms Lewinsky is the first of its kind in Britain. While television companies have paid for interviews with celebrities and pop stars, there has not, so far, been a case of such a huge sum being paid to someone who is in the news for a "journalistic" interview.
"If this amount is really being paid this marks the beginning of American- style tabloid television in Britain," an executive at a rival TV company said.
Britain's biggest news interviews have been conducted by the BBC's Panorama and its presenter, Martin Bashir. The interview with Diana, Princess of Wales, drew nearly 23 million viewers, while Louise Woodward attracted fewer than 7 million.
If Miss Lewinsky brings in 10 million viewers, it will be double the ratings Channel 4 secures for its top programme, the American sitcom Friends.
Mr Bashir was touted as the obvious candidate to interview Miss Lewinsky, but he is still under contract with the BBC, which was not prepared to enter the bidding war.
Mr Bashir has been offered $1.5m a year to join CNN, and has been courted by ITV companies, but he will have to sign a deal quickly if he is to interview Ms Lewinsky.