The winner of two Oscars for Women in Love and A Touch of Class was saying nothing officially about her next possible role, but it is understood she has been persuaded by private polling within the party to stand.
The polling showed that she would be a popular candidate for Labour alongside Ken Livingstone, the Brent East MP and former leader of the Greater London Council.
Ms Jackson, now 61, is seen as having a sufficiently high profile to win, while her current duties as Minister for Transport in London could give her the edge over her opponents on the transport problems that would need to be tackled by the new mayor.
Her son, Dan Hodges, said: "At the moment, these reports are pure speculation. However, obviously the Mayor of London is going to have a very important job and anyone offered the opportunity to go for such a role would have to consider it very carefully."
The MP for Hampstead and Highgate, may be seen as a "stop Ken" candidate, but friends said that she is not regarded as a "Blair babe". "She is seen as being loyal but she is not seen as being one of the 'Blair babes'. She has strong support among the grass roots. But we have to get the 'yes' vote first. It is important that it is a genuine campaign and not a beauty parade for the would-be candidates," said the source.
Ms Jackson will be campaigning for a "yes" vote in the referendum, before officially announcing her decision to stand. It would also mean giving up a ministerial career.
The field is expected to be crowded with several potential Tory candidates limbering up, including best-selling author, Lord Archer and Steve Norris, the former transport minister for London. The Liberal Democrat MP for Southwark and Bermondsey, Simon Hughes, is another possible candidate.
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