Ms Mowlam is being lined up for the post by Tony Blair in a government reshuffle aimed at exploiting her huge public popularity.
The move follows concern that Mr Cunningham has been damaged by the "drip- drip" effect of allegations about Concorde trips and spending, and his performance defending the Government's policy on genetically modified food. Although the Northern Ireland Secretary is currently heavily involved in the peace process, it is expected that she will be free to move in a summer reshuffle.
Downing Street hopes that by July the new Northern Ireland Executive will be running, and that a new Secretary of State can step in to take over the reins.
Tony Blair was tempted to promote Ms Mowlam last summer, but she insisted she wanted to see the peace process through to the creation this March of the Ulster executive outlined in the Good Friday Agreement.
She was also determined to steer the process through its most difficult hours after the Omagh bombing last year. With the latest difficulties on decommissioning, she is keen that nothing deflects her from the task at hand.
The 49-year-old MP for Redcar is seen by party strategists as one of Labour's most "voter friendly" assets and will represent the Government on television and radio.
Her promotion prospects were boosted last year when she presented a party political broadcast that resulted in a record number of membership applications for Labour.
She is also likely to take over a bigger role in campaign co-ordination once this year's round of elections to the European Parliament, local councils, Welsh Assembly and Scottish Parliament are over.
Her appointment as a party figurehead will mark the Government's determination to hold on to its big lead over the Conservatives as it focuses on the "delivery stage" in the run-up to the general election.
Mr Cunningham was moved from Agriculture to his Cabinet Office job to sort out ministerial disputes and "knock heads together". But his number two, Mr Blair's close friend Lord Falconer of Thoroton, has done most of the work co-ordinating Whitehall departments.
Mr Cunningham, who was a Labour minister in the 1970s, was brought in as an experienced operator capable of batting on "several wickets" at once, but he has not been judged a success in the role.
Downing Street believes he has done a competent job, but wants someone with more flair who is more readily associated with Labour's future rather than its past.
Ministers are also irritated that civil servants are continuing to leak details about Mr Cunningham to the press, a fact that was highlighted yesterday when it was revealed that he had moved an aide who objected to his use of taxpayers' money.
Neil Whitney, who worked within the minister's office, was moved after protesting that Mr Cunningham ordered up to six bottles of Macallan malt whisky at once for his drinks cabinet.
More seriously, he has been dogged with complaints about his use of luxury hotels and Concorde, disclosures believed to have been leaked by the staff of his successor at Agriculture, Nick Brown.
GM foods row, page 5