The Lewinsky deal is in the final stages of negotiation between the former White House intern's lawyers and Channel 4. However, it is understood Mr Bashir, renowned for securing big television interviews, willlobby Miss Lewinsky in an effort to persuade her that he, not Channel 4's Jon Snow, would be a better bet as an interviewer.
Channel 4 has agreed to pay Miss Lewinsky pounds 400,000 for the story of her affair with President Bill Clinton, and Granada is likely to have to put up a similar amount of cash to prevent its rival signing an agreement in the next few days.
It was confirmed on Monday Miss Lewinsky has agreed to a pounds 1m deal with the British author Andrew Morton to write her biography, which is expected to be published in February.
Mr Bashir's contract with Granada also means he will work with the newsreader Trevor McDonald on the station's new current affairs programme, 60 Minutes.
In the past, Mr Bashir has been criticised for being too soft in his lines of questioning, both to Princess Diana and Miss Woodward. However, the prominence of both interviews in Britain and America has meant that broadcasters have been offering high prices to secure a contract with him. Earlier this year he was offered $1.5m a year to join CNN.
While at the BBC, Mr Bashir was hamstrung in any efforts to secure the Lewinsky interview, as the corporation was not prepared to enter the bidding war. Industry insiders describe his move as a sign of a new sort of "tabloid television", in which broadcasters offer large sums to secure interviews with people in the news.