Coulson is understood to have turned down an offer of the editorship of the Daily Mirror after being persuaded by senior figures at News of the World owner News International that he is valued and can expect a long career at the Rupert Murdoch-owned firm.
The Daily Mirror is reportedly denying that any firm offer to Coulson has been made, but according to Media Guardian, Coulson was invited to take the job last week by Trinity Mirror general manager Ellis Watson, acting on instructions from chief executive Sly Bailey.
It is understood Coulson contacted News International executive chairman Les Hinton over the weekend to say he was rejecting the offer.
Coulson's decision would appear to leave the way open for firm favourite Weaver to take the Mirror job, although she is not the only name left in the frame.
Others understood to have been interviewed include the Daily Mirror's deputy editor Des Kelly, who has been covering the role following the sacking of Piers Morgan over the publishing of fake photographs of Iraqi prisoner abuse.
Also in the running is former News of the World and Hello! editor Phil Hall, who is now Trinity Mirror editorial director of magazines.
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