Mrs Beckett, the party's deputy and pro tem leader since the death of John Smith, will make her intentions known after Thursday's European elections.
Yesterday, she kept to Labour's prohibition on public comments before then and was said to have 'ruled nothing out or in', but supporters are convinced that she will eventually stand.
Although she has moved to the right politically, she would attract support from a number of 'soft' and traditional left MPs at the expense of John Prescott, the employment spokesman who is widely tipped to stand for both the leadership and deputy leadership.
Mrs Beckett would almost certainly offer herself for re-election as deputy leader as well, presaging a battle with Mr Prescott who is unlikely to beat Tony Blair, Labour's spokesman on home affairs, and now the sole candidate for leader from the party's 'modernising' wing.
A number of left-of-centre supporters of Robin Cook, trade and industry spokesman, would back Mrs Beckett in the expected event of him not standing, reducing Mr Prescott's share of the vote.
They are keen that the contest with Mr Blair should involve an alternative who could lay claim to prime ministerial qualities. While MPs played down any notion of tokenism yesterday, there would also be serious disquiet if there was no female leadership candidate.
Mr Cook remains officially undecided over whether to stand, but he has been urged to stand for the deputy leadership.
Ken Livingstone, the left-wing Campaign Group MP for Brent East, is also under pressure to stand for deputy, and is keen to do so if he can muster the necessary 35 nominations from MPs.Reuse content