Kirkcaldy’s Beveridge Park and Dunfermline’s Public Park have emerged as the frontrunners to accommodate the tribute, which was promised by Fife Council in the wake of the baby ashes scandal which first surfaced in 2012.
Riverside Park in Glenrothes, Townhill Park in Dunfermline, and Lochore Meadows Country Park were also among those on the shortlist, but it is understood those involved in creating the memorial consider the other two to be preferable.
Work on detailed designs will now be stepped up over the coming months, with architects expected to provide sketches of possible memorial areas most likely to feature a statue as a focal point and garden.
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Fife Council senior manager Alan Paul said the council is continuing to work with a small group of parents on how the important memorial might look - with the hope of using the outcome to engage with parents more widely.
He added: "Unfortunately we've not been able to consult face-to-face so we'll be arranging a virtual meeting to discuss proposals in the next few weeks."
Following revelations about shocking practices at Mortonhall Crematorium in Edinburgh, a subsequent investigation found that baby remains in Fife were either scattered in the crematoria gardens or in a lot of cases regrettably due to the cremation process at the time no remains were retrieved.
Dozens of parents across the region were awarded compensation as a result.
Fife Council apologised for the distress caused and pledged to work with parents and stakeholders on a fitting memorial to the babies - with a special working group set up to look at locations and what the memorial should look like.
A ‘weeping angel’ memorial had been initially looked at, but this design was discounted after further consultation with parents took place.
During that process, parents expressed a strong preference for a private but not isolated space in a public place where they could go for peace and to reflect, but urged the council not to procrastinate on locations when the actual memorial itself was more important.
Nevertheless, a preferred site will have to emerge and work will be done on considering the suitability and accessibility of chosen locations, as well as public transport links, security and the risk of anti-social behaviour, when coming to a final decision.