A second option, understood to have been favoured by Mr Burnham, would put the consultation back until early next year.
That raised questions among leaders over the impact on the local elections next May, however, while some councils - including Oldham and Stockport - could need longer than others to revisit their own particularly controversial proposals.
As a result a third, even longer delay, putting back consultation until next June, is also on the table.
That would mean no final draft would be published until at least December 2018 - and nothing formally adopted until Spring 2020.
Sources close to Mr Burnham said no decision had been reached on the timetable following Friday’s meeting, but stressed extra time was needed to get it right.
Last year’s consultation on the first draft drew 25,000 responses, huge numbers of which opposed building on the green belt. There was also considerable criticism of the plan’s methodology.
Mr Burnham’s office also believes the first version paid too little attention to building high-density housing in town centres, although attracting developers to those areas - where there is currently little investor interest - is not expected to be straightforward.
He believes the plan does not dovetail clearly enough with the region’s long-term visions for transport and affordable housing.
Delaying the plan in order to meet the mayor’s promises will raise questions over why last year’s consultation, which cost at least £80,000, was not put off until after he was elected.
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Meanwhile - in signs of emerging tensions following the mayoral election - it is understood around half the region’s council bosses do not want to see the plan delayed, particularly those confident in their existing proposals.
More than one senior insider suggested Mr Burnham had underestimated the level of work needed to fully re-think and re-write the plan, as pledged in his manifesto.
One warned the absence of such a masterplan would harm investor confidence, particularly in the wake of Brexit, since developers and businesses would not know where they stood.
The idea of delaying until 2020 was ‘ridiculous’, they added. A second said it was causing ‘frustration’ since ‘the timetable already existed’, adding: “Andy was fully briefed on this plan as an MP but he didn’t understand until now what he would have to deliver.”
Individual councils are now carrying out an initial review of their own parts of the draft masterplan, which originally included development on green belt in every part of the region.
That includes looking at land not currently included in green belt that could be re-designated in order to make up for losses elsewhere.